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FIVE-FIG-UBE TABLES 



OF 



MATHEMATICAL FUNCTIONS 



COMPRISING 



TABLES OP LOGARITHMS, POWERS OF NUMBERS, 

TRIGONOMETRIC, ELLIPTIC, AND OTHER 

TRANSCENDENTAL FUNCTIONS 



BY 



JOHN BORTHWIOK DALE, M.A. 

A88I8TANT PROFESSOR OF MATHEMATICS IN KTNOlB COLLBGft, 
UNIVERSITY OF LONDON 



EIGHTH IMPRESSION 



LONDON 

EDWARD ARNOLD 
41 AND 43 MADDOX STREET, BOND STREET, W. 

[All rights reserved] 



PREFACE. 



THIS collection of Tables has been formed chiefly with a view 
to meet the requirements of workers in Physical Science and 
Applied Mathematics. It includes many tables which have 
not hitherto found a place in such collections, while those 
tables which are of use only in Navigation have been excluded. 

For ordinary laboratory work four-figure tables of logarithms 
are at present generally employed. The small space they 
occupy renders them convenient to use, but they suffer from 
the defect that the accumulation of small errors frequently 
makes even the third significant figure in the result unreliable. 
For this reason five-figure tables are preferable. 

Four-figure tables give directly the logarithm for three 
significant figures, and, by differences, the logarithm for four; 
while five-figure tables usually give directly the logarithm for 
four significant figures, and so occupy ten times the space of 
a four-figure table. A glance, however, at the table in the 
following pages will show that it is only in the first third 
of it that the rapid variation of the differences renders a direct 
tabulation for four significant figures desirable. This has not 
been done, but merely the mean differences for each row have 
been tabulated, and these differences may be used when results 
accurate to four figures only are desired. Results accurate to 
five figures are to be obtained by using the Table of Anti- 
l^garithms; for it is precisely in that part of the Table of 



iv PREFACE. 

Logarithms where the variation is most rapid that the variation 
in the Table of the Inverse Function is slowest, and vice versa. 

The conjoint use of these Tables, therefore, offers all the 
accuracy obtainable with the usual five-figure tables, with the 
expenditure of little more labour than is involved in consulting 
a four-figure table. 

The principle stated above applies to several other pairs of 
Tables, such as those of Squares, Square Boots, Cubes, and Cube 
Eoots ; and by taking advantage of it, it has become possible 
to include a great number of tables within a moderate compass, 
without sacrificing convenience or accuracy. 

Several of the Tables have been constructed specially for 
this collection, and some others appear for the first time in 
their present form. Every care has been taken, and it is 
hoped they will be found free from error. 

J. BOETHWICK DALK 

NEW MALDEN, SURREY, 
December, 1903. 



CONTENTS. 



I. COMMON LOGARITHMS 1 

II. ANTILOGAHITHMS 4 

III. SQUARES * * 7 

IV. SQUARE BOOTS . 10 

V. CUBES .,.....*.. 16 

VL CUBE BOOTS 19 

VII. BECIPROCALS , ,28 

VIII. NATURAL LOGARITHMS OP 10 n AND 10"" . . .31 

IX. RECIPROCALS OF FACTORIALS ...... 31 

X. BERNOULLI'S NUMBERS .31 

XI. NATURAL SINES AND COSINES 32 

XII. NATURAL TANGENTS AND COTANGENTS . . . . 36 

XIII. NATURAL SECANTS AND COSECANTS 40 

XIV. LOGARITHMIC SINES AND COSINES ..... 44 
XV. LOGARITHMIC TANGENTS AND COTANGENTS ... 48 

XVI. LOGARITHMIC SECANTS AND COSECANTS . . . .52 

XVII. CIRCULAR, OB BADIAN MEASURE 56 

XVIII. CONVERSION OF TIME AND ANGULAR MEASURB . .59 
XIX. DECIMAL EQUIVALENTS ....... 60 

XX. NATURAL, OR NAPERIAN LOGARITHMS Gl 

XXL EXPONENTIAL FUNCTIONS, HYPERBOLIC SINES AND COSINES . 64 

XXII. Log u e- 66 

XXIII. (Log, tan (45 + =^- 3 ^ 67 



vi CONTENTS. 

PAQB 

XXIV. ELLIPTIC FUNCTIONS. F (9, <j>) 68 

XXV ELLIPTIC FUNCTIONS. E (0, <j>) 72 

XXVI. COMPLETE ELLIPTIC FUNCTIONS ...... 76 

XXVII. GAMMA FUNCTION . 77 

XXVIII. LOGARITHMS OF FACTORIALS 77 

XXIX. ZONAL SURFACE HARMONICS 78 

XXX. BESSEL FUNCTIONS. J (a?) AND J^a) 80 

XXXI. BESSEL FUNCTIONS. J N (a) c 81 

XXXII. BESSEL FUNCTIONS. !() 82 

XXXIII. BESSEL FUNCTIONS. ROOTS OF J n (a;), J (), AND J,() . 83 

XXXIV. BESSEL FUNCTIONS. VALUES OF J, + 1(&) . . . .83 

XXXV. NORMAL ERROR OR PROBABILITY INTEGRAL . '84 
XXXVI. EXPONENTIAL, COSINE AND SINE INTEGRALS . . . .85 

XXXVII. BINOMIAL COEFFICIENTS FOR INTERPOLATION BY DIFFERENCES 87 

XXXVIII. PROPORTIONAL PARTS 88 

XXXIX. NUMBERS USED IN CALCULATIONS 90 

EULER'S NUMBERS. E w 91 

EULER'S CONSTANT 91 

VALUES OF S n , W| T n< V w 92 

ENGLISH AND METRIC EQUIVALENTS . . . 92 



EIVE-FIGUBE TABLES 



OP 



MATHEMATICAL FUNCTIONS. 



EXPLANATION OF THE TABLES. 

I. LOGARITHMS OF NUMBERS. 

THE logarithms here tabulated are logarithms to the base 10, 
known as Briggian or Common Logarithms. 

The logarithm of a number consists of two parts, an integral 
part and a fractional part. The integral part is called the 
index, or characteristic ; the fractional part is called the mantissa. 

The characteristic of a number greater than 1 is the number 
one less than the number of digits in the integral part of the 
given number. 

The characteristic of a number less than 1 is negative and 
is the number one greater than the number of zeros following 
the decimal point. 

Ex. The characteristics of 5387, 5387, 0-0005387, are 3, 1, and -4 
respectively. 

The mantissa of all numbers having the same significant 
figures are the same. 

To find the mantissa of a given number. 

(a) If the number contains three significant figures, find 
the first two figures in the left-hand column of the table, and 
the third figure in the top row. The mantissa required will 



viii FIVE-FIGURE TABLES OF 

be found in the row containing the first two figures and in the 
column under the third figure. 

Ex. Log 53-8 = 1-73078. Log 0-00538 = 3-73078. 

The mantissa is always positive, and when it is preceded by 
a negative characteristic, the negative sign is written above the 
characteristic. 

(6) If the number contains four or five significant figures, 
find the mantissa corresponding to the first three figures as 
before. In the top row under Mean Differences find the fourth 
figure, and in the column under it, in the row containing the 
first two figures will be found the difference to be added to 
the mantissa. If there is a fifth figure, take the nearest tenth 
of the number corresponding to it in the Mean Difference 
columns, and add to the mantissa. 

Ex. To find log 53-874. 

Log 53-8 = 1-73078 

Diff. for 7 = 57 

Diff.for4 = 3 

Log 53-874 = 1-73138 

Near the beginning of the table the differences are large 
and change rapidly, and unless the third significant figure is 
4 or 5, the fifth figure of the mantissa obtained by using the 
mean differences will be incorrect. In this case the Table ot 
Antilogarithms may be used, or the Principle of Proportional 
Parts. 

Ex. To find log 120-73. 

Log 120 = 2-07918 
Log 121 = 2-08279 

Diff. for 1 = 361 

Diff. for 0-73 = 361 x 0-73 = 264 

Log 120-73 =2-08182 

The product 361 x 0*73 may be readily found by the 
Table of Proportional Parts at the end of the book. 

To find the number corresponding to a given logarithm. 

If the mantissa is found exactly in the tables, the first two 
significant figures of the number will be found in the same 
row at the left hand, and the third figure at the top of the 



MATHEMATICAL INUNCTIONS. ix 

column. The decimal point may then be placed by noting the 
value of the characteristic. 

If the mantissa is not found exactly in the tables, take out 
the next lower, and the three figures of the number belonging 
to it. Find the difference between this logarithm and the 
given one, and find the number corresponding to this difference 
in the same row under Mean Differences. If the difference is 
not found exactly, subtract the next lower, multiply the 
remainder by 10, and find the number corresponding to the 
product. 

Ex. Given logarithm = 1-73138 

Next lower logarithm = 1-73078 = log 53-8 

Diff. = CO 

Next lower difference = 57 = diff. for 7 

3 

30 = diff. for 4 
Therefore number is 53'874 



II. ANTILOGAKITHMS. 

In this table will be found the significant figures corre- 
sponding to given logarithms. The first two figures of the 
mantissa are found in the left-hand column, and the third in 
the top row. If there are more than three significant figures 
in the mantissa the corresponding differences will be found in 
the columns of Mean Differences. 

Ex. Given.logarithm = 2*08182 

2-081 = log 120-50 

Diff. for 8 = 22 

Diff. for 2 = 1 



2-08182 = log 120-73 

Near the end of the table, the differences are large and 
change rapidly. Hence, unless the third figure of the mantissa 
be 4 or 5, use the Table of Logarithms or the Principle of 
Proportional Parts. 

Use of the Tables of Logarithms and Antilogarithms. 

These tables may be used to perform multiplication, division, 



x FIVE-FIGURE TABLES OF 

involution, and root extraction in accordance with the following 
propositions : 

(1) Log A + log B = log (A x B) 
(ii.) Log A - log B = log (A ~- E) 
(iii.) n log A = log A n 

(iv.) i log -4 = log <X^4 

71 

NOTE.- When multiplying or dividing a logarithm whoso 
characteristic is negative, it is necessary to bear in mind that 
the mantissa is positive. 

Ex. (i.) 3-73138 x 3 = (-3 + 0-73138) x 3 = -9 + 2-19414 = 7-19414 
Ex. (ii 



III., IV., V., VI., VII. POWERS OF NUMBERS. 

These tables give the reciprocals, squares, and cubes of 
numbers between 1 and 10; the square roots of numbers 
between 1 and 100 ; and the cube roots of numbers between 
1 and 1000. 

The method of using them is essentially the same as that 
of using the Tables of Logarithms and Antilogarithms. 

The cubes of numbers containing four or five significant 
figures should be found by logarithms or by the Tables of Cube 
Boots. 



XL, XII., XIII. TKIGONOMETRICAL FUNCTIONS. 

These tables give the values of the natural sines, tangents, 
etc., for every third minute of the quadrant. The difference 
columns give the corrections for 1' and 2', 

The left-hand column of degrees and the top row of minutes 
are to be followed when sines, tangents, and secants are taken 
out 

The right-hand column of degrees and bottom row of 
minutes are to be used when cosines, cotangents, and cosecants 
are taken out 



MATHEMATICAL FUNCTIONS. xi 

Note that for the three co-functions, differences are to be 
subtracted. 

The integral part and decimal point are printed only in 
the columns headed 0' and 33'. 



XIV., XV., XVI. LOGARITHMIC TRIGONOMETRICAL FUNCTIONS. 

These tables give the logarithms of the numbers contained 
in the three preceding tables increased by 10, in order to avoid 
negative characteristics. 

The characteristic and decimal point are printed only in the 
columns headed 0' and 30'. 

Ex. Find sin 37 34' 12" and log sin 37 34' 12". 

Sin 37 33' = 0-60945 Log sin 37 33' = 9-78494 

Diff.forl' = 23 Diff. for 1' = 16 

Diff. for 12'' = 5 Diff. for 12" = 3 



Sin 37 34' 12" = 0-60973 Log sin 37 34' 12" = 9-78513 

When the values of the tangent, cotangent, secant, and 
cosecant are large and change rapidly, and are not given exactly 
in the tables, they should be found from the sine and cosine. 



Small Angles. 

The differences for the logarithmic sines and tangents of 
small angles are large and change rapidly. The values of the 
logarithms can be found by the following rules : 

(1) To obtain the log sine. 

Eeduce the angle to seconds, and to the logarithm of the 
number so obtained add 4*68557. From the sum subtract J of 
the log secant diminished by 10. 

(2) To obtain the log tangent. 

Eeduce the angle to seconds, and to the logarithm of the 
number so obtained add 4'68557. To the sum add of the log 
secant diminished by 10. 

(3) To obtain the angle, given the log sine. 

To the log sine add 5*31442 and J of the corresponding log 
secant diminished by 10. The sum is the logarithm of the 
number of seconds in the angle. 



xii FIVE-FIGURE TABLES OF 

(4) To obtain the angle, given the log tangent. 

To the log tangent add 5-31442 and subtract | of the corre- 
sponding log secant diminished by 10. The remainder is the 
logarithm of the number of seconds in the angle. 



VIII., XX. NATURAL LOGARITHMS. 

This table gives the logarithms of numbers to the base 
e (= 27182818 . . .). 

Every number may be expressed as the product of a 
number between 1 and 10, and some power of 10. The 
logarithm of the given number is the sum of the logarithms 
of the two factors. 

Ex. To find log, 735-2 and log, 0-0007352. 

735-2 = 7-352 x 10* 0-0007352 = 7-352 x 10'* 

Log, 7-35 = 1-99470 Log, 7-35 = 1-99470 

Diff.for2 = 27 Diff. for 2 27 

Log, 10 2 = 4-60517 Log, 10-* = 10-78966 

Log, 735-2 = 6-60014 Log 0-0007352 = 8-78463 



XXI., XXII., XXIII. EXPONENTIAL AND HYPERBOLIC 
FUNCTIONS. 

The values of e x , e~ x t cosh x, sinh x are tabulated at intervals 
of 0*01 from x = 1 to x = 3, and at intervals of 0*1 from x = 3 
to x = 6. 

The values of e x and e~* for greater values of x may be 
found from the table for Iog 10 e*. When e* = y y x = log. y. 
Hence these tables may be regarded as tables of antilogarithms 
for the base e. 

The hyperbolic functions are defined by the relations 



cosh x = (e* + "*) s i n h x = l( e * e ~*) 

tanh x = sinh x -7- cosh x, coth x = 1 -f- tanh x, 

sech x = 1 -7- cosh x, cech x = 1 -f- sinh x. 

When x is greater than 6, it is sufficiently accurate to take 
cosh x = sinh x = \e*. The hyperbolic functions m^y be 



MATHEMATICAL FUNCTIONS. xiii 

connected with the trigonometric functions by means of the table 
for u as lo tan 



cosh w = sec x, sinh w = tan x> tanh u = sin x. 



XXIV., XXV., XXVI. ELLIPTIC FUNCTIONS. 

<*> 

f cfo? 

These tables give the values of F(k, 6) = I 

I 

J 



. . 

v 1 - k* sin 2 a? 

_ 

and EQc, 0) = J y^i _ / C 2 S j n 2 ^ ^ f or every degree of the 

^ o 

amplitude ^>, and every fifth degree of 0, when sin =* k, the 
moefa^s. 

Table XXI. gives the values of the complete elliptic functions 

F l = F (k, |) and E^- E (k, ^), for every degree of 



9 = sirr 1 ^. 

(N.B. j^j is now generally denoted by K.) 
If u = F(k, 0), $ = am(^, A). 

k) = sin ^>, cn(w, k) = cos ^>, dn(w,*) 



Note sn(^, 1) = tanh u } cn(u, 1) = dn(?^, 1) = sech u. 



XXIX. ZONAL SURFACE HARMONICS. 

This table gives the values of the first seven harmonics for 
values of the argument x at intervals of O'Ol. 

P Q (x) = 1. Pi(*) = x. 

- 1). PB() = i(5^ - 3a?). 

3). 



- 5). 
P 7 (a?) = ^, 



xiv FIVE-FIGURE TABLES OF 



XXX. XXXIV. BESSEL FUNCTIONS. 

These tables give the values of J n (x) and also of 
I n (x) as i" n j n (tx) where i = \/ 1. 



XXXV. NORMAL ERROR OR PROBABILITY INTEGRAL. 

2 r* 

This table gives the values of the integral / = /- I e~ t2 dt. 

v 71 " J 



XXVII. GAMMA FUNCTIONS. 
This table gives the values of Iogi r(#) = log ] 

for values of x between 1 and 2. 

When x is greater than 2, the value may be obtained by 
using the formula of reduction 

r(x + 1) = ar(a) 

When x is large, the value of log, r(x + 1) is approximately 
given by 

log. r(x + 1) = log. \X2ir + (a + 4) lo & ~ a + 



1.2.a; 3 . 4.a? 5 . 6 . 



XXVIII. LOGARITHMS OF FACTORIALS. 

This table gives the values of log II(?i) = log x\ for integral 
values of x from x = 1 to x = 100, 
When x is integral Y(x + 1) = xl 
When x is large 



MATHEMATICAL FUNCTIONS. xv 

XXXVI. EXPONENTIAL, COSINE, AND SINE INTEGRALS. 
These tables give the values of the exponential integrals 

X "X 

J$i(x) = I du, and JEi(-x) = I du\ of the cosine integral 

* -co J - 

X X 

f cos u , , - , . . f sin M , 
i 0^ an d O f the sine integral I du. 

1 lv I Iv 

J / 

z 

The logarithmic integral Li(x) = I j = JSi(log x). 

J o 

Hence its values may be obtained from those of the exponential 
integral. 



X. BERNOULLI'S NUMBERS. 
These numbers are the coefficients in the expansion of 



x e* + 1 . ,1 r 

m the torm 
2 e* - 1 



[N.B. The notation varies, the series of numbers being 
sometimes written B\ 9 B 3 , B$ . . . -#a-i is the same as B n in 
the table here printed.] 



XXXVII. BINOMIAL COEFFICIENTS FOR INTERPOLATION BY 

DIFFERENCES. 

This table gives the values of the coefficients -^ ~- and 

X . 

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1 . -& . o 

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SINES. 



MKAJN 


DlKF. 


83' 


36' 


89' 


42' 


45' 


48' 


51' 


54' 


57' 


60' 





1' 


2' 


00960 


01047 


01134 


01222 


01309 


01396 


01483 


01571 


01658 


01745 


89 


29 


58 


02705 


02792 


02879 


02967 


03054 


03141 


03228 


03316 


03403 


03490 


88 


29 


58 


04449 


04536 


04623 


04711 


04798 


04885 


04972 


05059 


05146 


05234 


87 


29 


58 


06192 


06279 


06366 


06453 


06540 


06627 


06714 


06802 


06889 


06976 


86 


29 


58 


07933 


08020 


08107 


08194 


08281 


08368 


08455 


08542 


08629 


08716 


85 


29 


68 


09671 


09758 


09845 


09932 


10019 


10106 


10192 


10279 


10366 


10453 


84 


29 


58 


11407 


11494 


11580 


11667 


11754 


11840 


11927 


12014 


12100 


12187 


83 


29 


58 


13139 


13226 


13312 


13399 


13485 


13572 


13658 


13744 


13831 


13917 


82 


29 


58 


14867 


14954 


15040 


15126 


15212 


15299 


15385 


16471 


15557 


16643 


81 


29 


58 


16591 


16677 


16763 


16849 


16935 


17021 


17107 


17193 


17279 


17365 


80 


29 


57 


18309 


18395 


18481 


18567 


18652 


18738 


18824 


18910 


18995 


19081 


79 


29 


57 


20022 


20108 


20193 


20279 


20364 


20450 


20535 


20620 


20706 


20791 


78 


29 


57 


21729 


21814 


21899 


21985 


22070 


22155 


22240 


22325 


22410 


22495 


77 


28 


57 


23429 


23514 


23599 


28684 


237G9 


23853 


23938 


24023 


24108 


24192 


76 


28 


57 


25122 


25207 


25291 


25376 


25460 


25545 


25629 


25713 


25798 


25882 


75 


28 


56 


26808 


26892 


26976 


27060 


27144 


27228 


27342 


27396 


27480 


27564 


74 


28 


56 


28485 


28569 


28652 


28736 


28820 


28903 


28987 


29070 


29154 


29237 


73 


28 


56 


30154 


30237 


30320 


30403 


30486 


30570 


30653 


30736 


30819 


30902 


72 


28 


55 


31813 


31896 


31979 


32061 


32144 


32227 


32309 


32392 


32474 


32557 


71 


28 


55 


33463 


33545 


33G27 


33710 


33792 


33874 


33956 


34038 


34120 


34202 


70 


27 


55 


35102 


35184 


35266 


35347 


35429 


35511 


35592 


35674 


35755 


35837 


69 


27 


54 


36731 


36812 


36894 


36975 


37056 


37137 


37218 


37299 


37380 


37461 


68 


27 


54 


38349 


38430 


38510 


38591 


38671 


38752 


38832 


38912 


38993 


39073 


67 


27 


64 


39955 


40035 


40115 


40195 


40275 


40355 


40434 


40514 


40594 


40674 


66 


27 


63 


41549 


41628 


41707 


41787 


41866 


41945 


42024 


42104 


42183 


42262 


65 


26 


53 


43130 


43209 


43287 


43366 


43445 


43523 


43602 


43680 


43759 


43837 


64 


26 


52 


44698 


44776 


44854 


44932 


45010 


45088 


45166 


45243 


45321 


45399 


63 


26 


62 


46252 


46330 


46407 


46484 


46561 


46639 


46716 


46793 


46870 


46947 


62 


26 


51 


47793 


47869 


47946 


48022 


48099 


48175 


48252 


48328 


48405 


48481 


61 


26 


51 


49318 


49394 


49470 


4954G 


49622 


49697 


49773 


49849 


49924 


50000 


60 


25 


51 


50829 


50904 


50979 


51054 


51129 


51204 


51279 


51354 


61429 


51504 


59 


25 


50 


52324 


52399 


52473 


52547 


52621 


52696 


52770 


52844 


52918 


52992 


58 


25 


50 


53804 


53877 


53951 


54024 


54097 


54171 


54244 


54317 


54391 


54464 


57 


24 


49 


55266 


55339 


55412 


55484 


55557 


55630 


55702 


55775 


55847 


55919 


56 


24 


48 


56713 


56784 


56856 


56928 


57000 


57071 


57143 


57215 


57286 


67358 


55 


24 


48 


58141 


58212 


58283 


58354 


58425 


58496 


58567 


58637 


58708 


58779 


54 


24 


47 


59552 


59622 


69693 


69763 


59832 


51)902 


59972 


60042 


60112 


60182 


53 


23 


47 


60945 


61015 


61084 


61153 


61222 


61291 


61360 


61429 


61497 


61566 


52 


23 


46 


62320 


62388 


62456 


62524 


62592 


626GO 


62728 


62796 


62864 


62932 


'51 


23 


45 


63675 


^3742 


63810 


63877 


63944 


64011 


64078 


64145 


64212 


64279 


50 


22 


45 


65011 


65077 


65144 


65210 


65276 


65342 


65408 


65474 


65540 


65C06 


49 


22 


44 


66327 


66393 


66458 


66523 


66588 


66653 


66718 


66783 


66848 


66913 


48 


22 


43 


67623 


.67688 


67752 


67816 


67880 


67944 


68008 


68072 


68136 


68200 


47 


21 


43 


68899 


68962 


69025 


69088 


69151 


69214 


69277 


69340 


69403 


69466 


46 


21 


42 


70153 


70215 


70277 


70339 


70401 


70463 


70525 


70587 


70649 


70711 


45 


21 


41 


27' 


24' 


21' 


18' 


15' 


12' 


& 


ff 


y 


0' 





r 


2' 


MEAN 


COSINES. Drrp, 



34 



NATURAL 



MEAN 


DIFF. 





<y 


3' 


6* 


0' 


12' 


15' 


18' 


21' 


24* 


27' 


30' 


r 


2' 


45 


70711 


70772 


70834 


70896 


70957 


71019 


71080 


71141 


71203 


71264 


71325 


~20~ 


41 


46 


71984 


71995 


72055 


72116 


72176 


72236 


72297 


72367 


72417 


72477 


72537 


20 


40 


47 


73135 


73195 


73254 


73314 


73373 


73432 


73491 


73551 


73610 


73669 


73728 


20 


40 


48 


74314 


74373 


74431 


74489 


74548 


74606 


74664 


74722 


74780 


74838 


74896 


20 


89 


49 


75471 


75528 


75585 


75642 


75700 


75756 


75813 


75870 


75927 


75984 


76041 


19 


38 


50 


76604 


76661 


76717 


76772 


76828 


76884 


76940 


76996 


77051 


77107 


77162 


19 


37 


51 


77715 


77769 


77824 


77879 


77934 


77988 


78043 


78098 


78152 


78206 


78261 


18 


86 


52 


78801 


78855 


78908 


78962 


79016 


79069 


79122 


79176 


79_>29 


79282 


79335 


18 


86 


53 


79864 


79916 


79968 


80021 


80073 


80125 


80178 


80230 


80282 


80334 


80386 


17 


35 


54 


80902 


80953 


81004 


81055 


81106 


81157 


81208 


81259 


81310 


81361 


81412 


17 


34 


55 


81915 


81965 


82015 


82065 


82115 


82165 


82214 


82264 


82314 


82363 


82413 


17 


83 


56 


82904 


82953 


83001 


83050 


83098 


83147 


83195 


83244 


83292 


83340 


83389 


16 


32 


57 


83867 


83915 


83902 


84009 


84057 


84104 


84151 


84198 


84245 


84292 


84339 


16 


31 


58 


84805 


84851 


84897 


84943 


84989 


85035 


85081 


85127 


85173 


85218 


85264 


15 


31 


50 


85717 


85762 


85806 


85851 


85396 


85941 


85985 


86030 


86074 


86119 


86163 


15 


30 


60 


86603 


86646 


86690 


86733 


86777 


86820 


86863 


86906 


86949 


86993 


87036 


14 


29 


61 


87462 


87504 


87540 


87589 


87631 


87673 


87715 


87756 


87798 


87840 


87882 


14 


28 


62 


;88295 


88336 


88377 


88417 


88458 


88499 


88539 


88580 


88620 


88661 


88701 


14 


27 


63 


81H01 


89140 


89180 


89219 


89259 


89298 


89337 


89376 


89415 


89454 


89493 


13 


26 


64 


89879 


89918 


89956 


89994 


90032 


90070 


90108 


90146 


90183 


90221 


90259 


13 


25 


65 


90631 


90668 


90704 


90741 


90778 


90814 


90851 


90887 


90924 


90960 


90996 


12 


24 


66 


91355 


91390 


91425 


91461 


91496 


91531 


915C6 


91601 


91636 


91671 


91706 


12 


23 


67 


92050 


92085 


92119 


92152 


92186 


92220 


92254 


92287 


92321 


92355 


92388 


11 


23 


68 


92718 


92751 


92784 


92816 


92849 


92881 


92913 


92945 


92978 


93010 


93042 


11 


22 


60 


93358 


93389 


93420 


93452 


93483 


93514 


93544 


93575 


93606 


93637 


93667 


10 


21 


70 


93969 


93999 


94029 


94058 


94088 


94118 


94147 


94176 


94206 


94235 


94264 


10 


20 


71 


94552 


94580 


94609 


94637 


94665 


94693 


94721 


94749 


94777 


94805 


94832 


9 


19 


72 


95106 


95133 


95159 


95186 


95213 


95240 


95266 


95293 


95319 


95345 


95372 


9 


18 


73 


95630 


95656 


95681 


95707 


95732 


95757 


95782 


95807 


95832 


95857 


95882 


8 


17 


74 


96126 


96150 


96174 


96198 


96222 


96246 


96269 


96293 


96316 


96340 


90363 


8 


16 


75 


96593 


96615 


96638 


96660 


96682 


96705 


96727 


96749 


96771 


96793 


96815 


7 


15 


76 


97030 


97051 


97072 


97093 


97113 


97134 


97155 


97176 


97196 


97217 


97237 


7 


14 


77 


97437 


97457 


97476 


97496 


97515 


97534 


97553 


97573 


97592 


97611 


97630 


6 


13 


78 


97815 


97833 


97851 


97869 


97887 


97905 


97922 


97940 


97958 


97975 


97992 


6 


12 


70 


98163 


98179 


98196 


98212 


98229 


98245 


98261 


98277 


98294 


98310 


98325 


5 


11 


80 


98481 


98496 


98511 


98526 


98541 


98556 


98570 


98585 


98600 


98614 


98629 


5 


10 


81 


98769 


98782 


98796 


98809 


98823 


98836 


98849 


98868 


98876 


98889 


98902 


4 


9 


82 


99027 


99039 


99051 


99063 


99075 


99087 


99098 


99110 


99122 


99133 


99144 


4 


8 


83 


9S255 


99265 


99276 


99286 


99297 


99307 


99317 


99327 


99337 


99347 


99357 


3 


7 


84 


99452 


W461 


99470 


99479 


99488 


99497 


99506 


99514 


99523 


99531 


99540 


3 


6 


85 


99619 


99627 


99635 


99642 


99649 


99657 


99664 


99671 


99678 


99685 


99692 


2 


5 


86 


99756 


99762 


99768 


99774 


99780 


99786 


99792 


99797 


99803 


99808 


99813 


2 


4 


87 


99863 


99867 


99872 


99876 


99881 


99885 


99889 


99893 


99897 


99901 


99905 


1 


3 


88 


99939 


99942 


99945 


99948 


99951 


99953 


99956 


99959 


99961 


99963 


99966 


1 


2 


80 


99985 


99986 


99988 


99989 


99990 


49991 


99993 


99994 


99995 


99995 


99996 





1 





60' 


57' 


54' 


51' 


48' 


45' 


42' 


30' 


36' 


83' 


3<y 


r 


2' 


MEAN 


NATURAL DIFF. 



SINES continued. 



MEAN 


DIFF. 


83' 


36' 


30' 


42* 


46 f 


48' 


6V 


54' 


67' 


6(X 


o 


1' 


2' 


71386 


71447 


71508 


71569 


71630 


71691 


71752 


71813 


71873 


71984 


44 


20 


41 


72597 


72657 


72717 


72777 


72837 


72897 


72957 


73016 


73076 


73135 


43 


20 


40 


73787 


73846 


73904 


73963 


74022 


74080 


74139 


74198 


74256 


74314 


42 


20 


39 


74953 


75011 


75069 


75126 


75184 


75241 


75299 


75356 


75414 


75471 


41 


19 


38 


76097 


76154 


76210 


76267 


76323 


76380 


76436 


76492 


76548 


76604 


40 


19 


38 


77218 


77273 


77329 


77384 


77439 


77494 


77550 


77605 


77660 


77715 


39 


18 


37 


78315 


78369 


78424 


78478 


78532 


78586 


78640 


78694 


78747 


78801 


38 


18 


36 


79388 


79441 


79494 


79547 


79600 


79653 


79706 


79758 


79811 


79864 


37 


18 


35 


80438 


80489 


80541 


80593 


80644 


80696 


80748 


80799 


80850 


80902 


36 


17 


34 


81462 


81513 


81563 


81614 


81664 


81714 


81765 


81815 


81865 


81915 


35 


17 


34 


82462 


82511 


82561 


82610 


82659 


82708 


82757 


82806 


82855 


82904 


34 


16 


33 


83437 


83485 


83533 


83581 


83629 


83076 


83724 


83772 


83819 


83867 


33 


16 


32 


84386 


84433 


84480 


84526 


84573 


84G19 


84666 


84712 


84759 


84805 


32 


16 


31 


85310 


85355 


85401 


85446 


85491 


85536 


85582 


85627 


85672 


85717 


31 


15 


30 


86207 


86251 


86295 


86340 


86384 


86427 


86471 


86515 


86559 


8C603 


30 


15 


29 


87079 


87121 


87164 


87207 


87250 


87292 


87335 


87377 


87420 


87462 


29 


14 


28 


87923 


87965 


88006 


88048 


88089 


88130 


88172 


88213 


88254 


88295 


28 


14 


28 


88741 


88782 


88822 


88862 


88002 


88942 


88981 


89021 


80001 


80101 


27 


13 


27 


89532 


89571 


89610 


89649 


89087 


89726 


89704 


89803 


80841 


80879 


26 


13 


26 


90296 


90334 


90371 


90408 


90446 


90483 


90520 


90557 


90504 


90631 


25 


12 


26 


91032 


91068 


91104 


91140 


91176 


91212 


91248 


91283 


01319 


01355 


24 


12 


24 


91741 


91775 


91810 


91845 


91879 


91914 


911)48 


91082 


92016 


02050 


23 


11 


23 


92421 


92455 


92488 


92521 


92554 


92587 


92G20 


92058 


92086 


02718 


22 


11 


22 


93074 


93106 


93137 


93169 


93201 


93232 


93264 


93295 


93327 


03358 


21 


10 


21 


93698 


93728 


93759 


93789 


93819 


93849 


93879 


93909 


93939 


93969 


20 


10 


20 


94293 


94322 


94351 


94380 


94409 


94438 


94466 


94495 


94523 


9-1552 


19 


10 


19 


94860 


94888 


94915 


94943 


94970 


94997 


95024 


95052 


95079 


95106 


18 


9 


18 


95398 


95424 


95450 


95476 


95502 


95528 


95554 


95579 


95605 


95030 


17 


9 


17 


95907 


95931 


95956 


95981 


96005 


96029 


96054 


96078 


06102 


96126 


16 


8 


16 


96J86 


96410 


96433 


96456 


96479 


96502 


96524 


96547 


90570 


96593 


15 


8 


15 


96837 


96858 


96880 


96902 


D6923 


96945 


90966 


90987 


97008 


97030 


14 


7 


14 


97257 


97278 


87298 


97318 


973,38 


97353 


97378 


07398 


07417 


97437 


13 


7 


13 


97648 


97667 


97686 


97705 


97723 


97742 


97760 


97778 


07707 


97815 


12 


6 


12 


98010 


98027 


98044 


98061 


98079 


98096 


98112 


98129 


98146 


98103 


11 


6 


11 


98341 


98357 


98373 


98389 


98404 


98420 


98435 


98450 


98406 


98481 


10 


5 


10 


98643 


98657 


98671 


98686 


98700 


98714 


98728 


98741 


98755 


98760 


9 


5 


9 


98914 


98927 


98940 


98953 


98965 


98978 


98990 


99002 


99015 


99027 


8 


4 


8 


99166 


99167 


99178 


99189 


99200 


99211 


99222 


99233 


99244 


09255 


7 


4 


7 


99367 


99377 


99386 


99396 


99406 


99415 


99424 


99434 


99443 


99452 


6 


3 


6 


99548 


99556 


99564 


99572 


99580 


99588 


99596 


99604 


99612 


99619 


5 


3 


6 


99699 


09705 


99712 


99719 


99725 


99731 


99738 


99744 


99750 


99766 


4 


2 


4 


99819 


99824 


99829 


99834 


99839 


99844 


99849 


99854 


99858 


99863 


3 


2 


3 


99909 


99912 


99916 


99919 


99923 


99926 


99930 


99933 


99936 


99939 


2 


1 


2 


99968 


99970 


99972 


99974 


99976 


99978 


99980 


99982 


99983 


99985 


1 


1 


1 


99997 


99998 


99998 


99999 


99999 


99999 


00000 


L'OOOOO 


00000 


00000 











27' 


24' 


21' 


18' 


16' 


12' 


9' 


e' 


3' 


0' 





r 


2' 


MEAN 


COSINES. DIFF. 



XII.-NATURAL 



MEAN 


DIFF. 





0' 


3' 


6* 


9' 


12' 


15' 


18' 


21' 


24' 


27' 


30' 


r 


2' 





ooooo 


00087 


00175 


00262 


00349 


00436 


00524 


00611 


00698 


00785 


00873 


29 


58 




01746 


01833 


01920 


02007 


02095 


02182 


02269 


02357 


02444 


02531 


02619 


29 


58 


2 


03492 


03579 


03667 


03754 


03842 


03929 


04016 


04104 


04191 


04279 


04366 


29 


58 


3 


05241 


05328 


05416 


05503 


05591 


05678 


05766 


05854 


05941 


06029 


06116 


29 


58 


4 


06993 


07080 


07168 


07256 


07344 


07431 


07519 


07607 


07695 


07782 


07870 


29 


58 


5 


08749 


08837 


08925 


09013 


09101 


09189 


09277 


09365 


09453 


09541 


09629 


29 


59 


6 


10510 


10599 


10687 


10775 


10863 


10952 


11040 


11128 


11217 


11305 


11394 


29 


59 


7 


12278 


12367 


12456 


12544 


12633 


12722 


12810 


12899 


12988 


18076 


13165 


30 


59 


8 


14054 


14143 


14232 


14321 


14410 


14499 


14588 


14678 


14767 


14856 


14945 


30 


59 


9 


15838 


15928 


16017 


16107 


16196 


16286 


16376 


164G5 


16555 


16645 


16734 


30 


60 


10 


17633 


17723 


17813 


17903 


17993 


18083 


18173 


18263 


18353 


18444 


18534 


30 


60 


11 


19438 


19529 


19619 


19710 


19801 


19891 


19982 


20073 


20164 


20254 


20345 


30 


60 


12 


21256 


21347 


21438 


21529 


21621 


21712 


21804 


21895 


21986 


22078 


22 169 


30 


61 


13 


23087 


23179 


23271 


23363 


23155 


23547 


23G39 


23731 


23823 


23916 


2-1008 


31 


Gl 


14 


24933 


25026 


25118 


25211 


25304 


25397 


25490 


26583 


25676 


25769 


25862 


31 


62 


15 


26795 


26888 


26982 


27076 


27169 


27263 


27357 


27451 


27545 


27638 


27732 


31 


62 


16 


28675 


28769 


28864 


28958 


29053 


29147 


29242 


29337 


29432 


29526 


29621 


32 


G3 


17 


30573 


30669 


30764 


30860 


30955 


31051 


31147 


31242 


31338 


31434 


31530 


32 


64 


18 


32492 


32588 


32685 


32782 


32878 


32975 


33072 


33169 


33266 


33363 


33460 


32 


65 


19 


34433 


34530 


34628 


34726 


34824 


34922 


35020 


35118 


35216 


35314 


35412 


33 


65 


20 


36397 


36496 


36595 


36694 


36793 


36892 


3G991 


37090 


37190 


37289 


37388 


33 


66 


21 


38386 


38487 


38587 


38687 


38787 


38888 


38988 


39089 


39190 


39290 


39391 


34 


67 


22 


40403 


40504 


40606 


40707 


40809 


40911 


41013 


41115 


41217 


41319 


41421 


34 


68 


23 


42447 


42551 


42654 


42757 


428CO 


42963 


43067 


43170 


43274 


431578 


43181 


34 


09 


24 


44523 


44G27 


44732 


44837 


44942 


45047 


45152 


45257 


45362 


45467 


45573 


35 


70 


25 


46631 


46737 


46843 


46950 


47056 


47163 


47270 


47377 


47483 


47590 


47698 


36 


71 


26 


48773 


48881 


48989 


49098 


49206 


49315 


49423 


49532 


49640 


49749 


49858 


36 


72 


27 


50953 


51063 


51173 


51283 


51393 


51503 


51614 


51724 


51835 


5194G 


52057 


37 


73 


28 


53171 


53283 


53395 


53507 


53620 


53732 


53844 


53'J57 


54070 


54183 


54296 


37 


75 


29 


55431 


55545 


55659 


55774 


55888 


5G003 


56117 


56232 


5G347 


56462 


56577 


38 


77 


30 


57735 


57851 


57968 


58085 


58201 


58318 


58435 


58552 


5H670 


58787 


58905 


39 


78 


31 


60086 


60205 


60324 


60443 


60562 


60681 


60801 


G0921 


61040 


61160 


61280 


40 


79 


32 


62487 


62608 


62730 


62852 


G2973 


63095 


63217 


63340 


G34G2 


63584 


63707 


41 


81 


33 


64941 


65065 


65189 


65314 


65438 


65563 


65688 


65813 


659,'J8 


GGOG3 


66189 


42 


83 


34 


67451 


67578 


67705 


67832 


67960 


68088 


68215 


68343 


68471 


G8GOO 


68728 


43 


85 


35 


70021 


70151 


70281 


70412 


70542 


70673 


70804 


70935 


71066 


71198 


71329 


44 


87 


36 


72654 


72788 


72921 


73055 


73189 


73323 


73457 


73592 


73726 


73861 


73996 


45 


89 


87 


75355 


75492 


75629 


75767 


75904 


76042 


76180 


76318 


76456 


76594 


76733 


46 


92 


38 


78129 


78269 


78410 


78551 


78G92 


78834 


78975 


79117 


79259 


79401 


79544 


47 


95 


39 


80978 


81123 


81268 


81413 


81558 


81703 


81849 


81995 


82141 


82287 


82434 


48 


97 


40 


83910 


84059 


84208 


84357 


84507 


84656 


84806 


84956 


85107 


85257 


85408 


50 


99 


41 


86929 


87082 


87236 


87389 


87543 


87698 


87852 


88007 


88162 


88317 


88473 


52 


103 


42 


90040 


90199 


90357 


90516 


90674 


90834 


90993 


91153 


91313 


91473 


91633 


53 


107 


43 


93252 


93415 


93578 


93742 


93906 


94071 


94235 


94400 


94565 


94731 


9489G 


55 


110 


44 


96569 


96738 


96907 


97076 


97246 


97416 


97686 


97756 


97927 


98098 


98270 


57 


113 





60' 


57' 


54' 


51' 


48' 


45' 


42' 


39' 


36' 


33' 


30' 


r 


2' 


MEAN 


NATURAL DIFF. 



TANGENTS. 



MEAN 


DlFF. 


83* 


86' 


89' 


42' 


45' 


48' 


51' 


54' 


67' 


60' 





r 


2' 


00960 


01047 


01135 


01222 


01309 


01396 


01484 


01571 


01658 


01746 


89 


29 


58 


02706 


02793 


02881 


02968 


03055 


03143 


03230 


03317 


03405 


03492 


88 


29 


58 


04454 


04541 


04628 


04716 


04803 


04891 


04978 


05066 


05153 


05241 


87 


29 


58 


OG204 


06291 


06379 


06467 


06554 


06642 


06730 


06817 


06905 


06993 


86 


29 


68 


07958 


08046 


08134 


08221 


08309 


08397 


08485 


08573 


08661 


08749 


85 


29 


59 


09717 


09805 


09893 


09981 


10069 


10158 


10246 


10334 


10422 


10510 


84 


29 


59 


11482 


11570 


11659 


11747 


11836 


11924 


12013 


12101 


12190 


12278 


88 


29 


69 


13254 


13343 


13432 


13521 


13609 


13698 


13787 


13876 


13965 


14054 


82 


30 


59 


15034 


15124 


15213 


15302 


15391 


15481 


15670 


15660 


15749 


15838 


81 


30 


60 


16824 


16914 


17004 


17093 


17183 


17273 


17363 


17453 


17543 


17633 


80 


30 


60 


18624 


18714 


18805 


18895 


18986 


19076 


19166 


19257 


19347 


19438 


79 


30 


60 


20436 


20527 


20618 


20709 


20800 


20891 


20982 


21073 


21164 


21256 


78 


30 


61 


22261 


22353 


22444 


22536 


22628 


22719 


22811 


22903 


22995 


23087 


77 


31 


61 


24100 


24193 


24285 


24377 


24470 


24562 


24655 


24747 


24840 


24933 


76 


31 


61 


25955 


26048 


26141 


26235 


26328 


26421 


26515 


26608 


26701 


26795 


75 


31 


62 


27826 


27921 


28015 


28109 


28203 


28297 


28B91 


28486 


28580 


28675 


74 


31 


63 


29716 


29811 


29906 


30001 


30097 


30192 


30287 


30382 


30478 


30673 


73 


32 


63 


31626 


31722 


31818 


31914 


32010 


32106 


32203 


32299 


32396 


32492 


72 


32 


64 


33557 


33654 


33751 


33848 


33945 


31043 


34140 


34238 


34335 


34433 


71 


32 


65 


35510 


35608 


35707 


35805 


35904 


36002 


36101 


36199 


36298 


36397 


70 


33 


66 


37488 


37588 


37687 


37787 


37887 


37986 


38086 


38186 


38286 


38386 


69 


33 


67 


39492 


39593 


39694 


39795 


39896 


39997 


40098 


40200 


40301 


40403 


68 


34 


67 


41524 


41626 


41728 


41831 


41933 


42036 


42139 


42242 


42345 


42447 


67 


34 


68 


43585 


43689 


43793 


43897 


44001 


44105 


44210 


44314 


44418 


44523 


66 


35 


69 


45678 


45784 


45889 


45995 


46101 


46206 


46312 


46418 


46525 


46631 


65 


35 


71 


47805 


47912 


48019 


48127 


48234 


48342 


48450 


48557 


48665 


48773 


64 


36 


71 


49967 


50076 


50185 


50295 


50404 


50514 


50623 


50733 


50843 


50953 


63 


36 


73 


52168 


52279 


52390 


52501 


52613 


52724 


52836 


52947 


53059 


53171 


62 


37 


76 


54409 


54522 


54635 


54748 


54862 


54975 


55089 


55203 


55317 


55431 


61 


38 


76 


56693 


56808 


56923 


57039 


57155 


57271 


57386 


57503 


57619 


57735 


60 


39 


77 


69022 


69140 


59258 


59376 


59494 


59612 


59730 


69849 


59967 


60086 


59 


89 


79 


61400 


61520 


61641 


61761 


61882 


62003 


62124 


62245 


62366 


62487 


58 


40 


81 


63830 


63953 


64076 


64199 


64322 


(54446 


64569 


64693 


64817 


64941 


57 


41 


82 


66314 


66440 


66566 


66692 


66818 


60944 


67071 


67197 


67324 


67451 


56 


42 


84 


68857 


68985 


69114 


69243 


69372 


69502 


69631 


69761 


69891 


70021 


55 


43 


86 


71461 


71593 


71725 


71857 


71990 


72122 


72255 


72388 


72521 


72654 


54 


44 


89 


74131 


74267 


74402 


74538 


74674 


74810 


74946 


75082 


75219 


75355 


53 


45 


91 


76871 


77010 


77149 


77289 


77428 


77568 


77708 


77848 


77988 


78129 


52 


46 


93 


79686 


79829 


79972 


80115 


80258 


80402 


80546 


80690 


80834 


80978 


51 


48 


95 


82580 


82727 


82874 


83022 


83169 


83317 


83465 


83613 


83761 


83910 


50 


49 


98 


85559 


85710 


85862 


86014 


86166 


86318 


86470 


86623 


86776 


86929 


49 


51 


101 


88628 


88784 


88940 


89097 


89253 


89410 


89567 


89725 


89883 


90040 


48 


52 


104 


91794 


91955 


92116 


92277 


92439 


92601 


92763 


92926 


93088 


93252 


47 


54 


108 


95062 


95229 


95395 


95562 


95729 


95897 


96064 


96232 


96400 


96569 


46 


56 


111 


98441 


98613 


98786 


98958 


99131 


99304 


99478 


99652 


99826 


I'OOOOO 


45 


58 


115 


27' 


24' 


21' 


18' 


15' 


12' 


0' 


6' 


8' 


0' 





r 


2' 


MEAN 


COTANGENTS. DOT. 



NATURAL 



MEAN 




DiTF. 


o 


0' 


8* 


6' 


& 


12' 


15' 


18' 


21' 


24' 


27' 


30' 


r 


2' 


45 


1-00000 


00175 


00350 


00525 


00701 


00876 


01053 


01229 


01406 


01583 


01761 


58 


117 


46 


1-03553 


03734 


03915 


04097 


04279 


04461 


04644 


04827 


05010 


05194 


05378 


61 


121 


47 


1-07237 


07425 


07613 


07801 


07990 


08179 


08369 


08559 


08749 


08940 


09131 


63 


126 


48 


1-11061 


11256 


11452 


11648 


11844 


12041 


12238 


12435 


12633 


12831 


13029 


66 


131 


49 


M6037 


16240 


15443 


15647 


15851 


16056 


16261 


16466 


16672 


16878 


17085 


68 


137 


50 


1-19175 


19387 


19599 


19811 


20024 


20237 


20451 


20665 


20879 


21094 


21310 


71 


142 


51 


1-23490 


23710 


23931 


24153 


24375 


24597 


24820 


25044 


25268 


25492 


25717 


74 


148 


52 


1-27994 


28225 


28456 


28687 


28919 


29152 


29385 


29618 


29853 


30087 


30323 


78 


155 


53 


1-32704 


32946 


83187 


33430 


33673 


33916 


34160 


34405 


34650 


34896 


35142 


81 


162 


54 


1-37638 


37891 


38145 


38399 


38653 


38909 


39165 


39421 


39679 


39936 


40195 


85 


169 


55 


1'42816 


43080 


43347 


43614 


43881 


44149 


44418 


44688 


44958 


45229 


45501 


89 


179 


56 


1-48256 


48536 


48816 


49097 


49378 


49661 


49944 


50228 


50512 


50797 


51084 


94 


189 


57 


1-53986 


54281 


54576 


54873 


55170 


55467 


55766 


56065 


56366 


56667 


5G969 


99 


198 


58 


1-60033 


60345 


60657 


60970 


61283 


61598 


61914 


62230 


62548 


62866 


63185 


105 


210 


59 


1-66428 


66757 


67088 


67419 


67752 


68085 


68419 


68754 


69091 


69428 


69766 


111 


222 


60 


1-73205 


73555 


73905 


74257 


74610 


74964 


75319 


75675 


76032 


7fi390 


76749 


118 


236 


61 


1-80405 


80777 


81150 


81524 


81899 


82276 


82654 


83033 


83413 


83794 


84177 


126 


251 


62 


1-88073 


88469 


88867 


89266 


89667 


900C9 


90472 


90876 


91282 


91 090 


92098 


134 


2G8 


63 


1-96261 


96685 


97111 


97538 


57966 


98.196 


98828 


99261 


99695 


OOT31 


00569 


143 


287 


64 


2-05030 


05485 


05942 


06400 


06860 


07321 


07785 


08250 


08716 


09184 


09G54 


154 


307 


65 


2-14451 


14940 


15432 


15925 


16420 


16917 


17416 


17916 


18419 


18923 


19430 


1(56 


331 


66 


2-24604 


25132 


25663 


26196 


26730 


27267 


27806 


28348 


28891 


29437 


29984 


179 


358 


67 


2-35585 


36158 


3C733 


37311 


37891 


38473 


39058 


39645 


40235 


40827 


41421 


194 


388 


68 


2-47509 


48132 


48758 


49386 


50018 


50652 


61289 


51929 


52571 


53217 


53865 






69 


2-60509 


61190 


61874 


625G1 


63252 


63945 


64612 


65342 


66046 


66752 


67462 






70 


2-74748 


75496 


76247 


77002 


77761 


78523 


79289 


80059 


80833 


81610 


82391 






71 


2-90421 


91246 


92076 


92910 


93748 


94591 


95437 


96288 


97144 


98004 


98868 






72 


3-07768 


08685 


09606 


10532 


11464 


12400 


13341 


14288 


15240 


16197 


17159 






73 


3-27085 


28109 


29139 


30174 


31216 


32264 


33317 


34377 


35443 


36536 


37594 






74 


3-48741 


49894 


51053 


52219 


53393 


54573 


55761 


56957 


58160 


59370 


60588 






75 


3-73205 


74512 


75828 


77152 


78485 


79827 


81177 


82537 


83906 


85284 


86671 






76 


4-01078 


02574 


04081 


05599 


07127 


08666 


10216 


11778 


13350 


14934 


16530 






77 


4-33148 


34879 


36623 


38381 


40152 


41936 


43735 


45548 


47374 


49215 


51071 






78 


4-70463 


72490 


74534 


76595 


78673 


80769 


82882 


85013 


87162 


89330 


91516 






79 


5-14455 


16863 


19293 


21744 


24218 


26715 


29235 


31778 


34345 


36936 


39552 






80 


5-67128 


70037 


72974 


75941 


78938 


81966 


85024 


83114 


91236 


94390 


97576 






81 


6-31375 


34961 


38587 


42253 


45961 


49710 


53503 


57339 


61219 


65144 


69116 






82 


7-11537 


16071 


20661 


25310 


30018 


34786 


39616 


44509 


49465 


54487 


69575 






83 


8-14435 


20352 


26355 


32446 


38625 


44896 


51259 


57718 


64275 


70931 


77689 






84 


9-51436 


59490 


67680 


76009 


84482 


93101 


10-019 


10-108 


10-199 


10-291 


10-385 






85 


11-430 


11-546 


11-664 


11-785 


11-909 


12-035 


12-163 


12-295 


12-429 


12-566 


12-706 






86 


14-301 


14-482 


14-669 


14-860 


15-056 


15-257 


15-464 


15-676 


16-895 


16-119 


16-350 






87 


19-081 


19-405 


19-740 


20-087 


20-446 


20-819 


21-205 


21-606 


22-022 


22-454 


22-904 





88 


28-636 


29-371 


30-145 


30-960 


31-821 


32-730 


33-694 


34-715 


85-801 


36-956 


38-188 






89 


57-290 


60-306 


63-657 


67-402 


71-615 


76-390 


81-847 


88-144 


95-489 


104-17 


114-59 









60' 


57' 


54' 


51' 


48' 


45' 


42' 


39' 


36' 


33' 


30' 


1' 


2* 


MEAN 


NATURAL Diif. 



39 



MEAN 



33 1 


36* 


39' 


42' 


45' 


48' 


51' 


64' 


57' 


60' 





r 


2' 


1-01939 


02117 


02295 


02474 


02653 


02832 


03012 


03192 


03372 


03553 


44 


60 


119 


1-05562 


05747 


05932 


06117 


06303 


06489 


06676 


06862 


07049 


07237 


43 


62 


124 


1-09322 


09514 


09706 


09899 


10091 


10285 


10478 


10672 


10867 


11061 


42 


64 


128 


1-13228 


13428 


13627 


13828 


14028 


14229 


14430 


14632 


14834 


15037 


41 


67 


133 


1-17292 


17600 


17708 


17916 


18125 


18334 


18544 


18754 


18964 


19176 


40 


70 


139 


1-21526 


21742 


21959 


22176 


22394 


22612 


22831 


23050 


23270 


23490 


39 


73 


145 


1-25943 


26169 


26395 


26622 


26849 


27077 


27306 


27535 


27764 


27994 


38 


70 


151 


1-30558 


30795 


31031 


31269 


31507 


31745 


31984 


32224 


32464 


32704 


37 


79 


159 


1-35389 


35637 


35885 


36134 


36383 


36633 


36883 


37134 


37386 


37638 


36 


83 


166 


1-40454 


40714 


40974 


41235 


41497 


41759 


42022 


42286 


42550 


42815 


35 


87 


175 


1-45773 


46046 


46320 


46595 


4C870 


47146 


47422 


47699 


47977 


48256 


34 


92 


183 


1-51370 


51658 


51946 


52235 


52525 


52816 


53107 


53400 


53693 


53986 


33 


97 


193 


1-57271 


57575 


57879 


58184 


58490 


58797 


59105 


69414 


59723 


60033 


32 


102 


204 


1-63505 


63826 


64148 


64471 


64795 


65120 


65445 


65772 


66099 


66428 


31 


108 


216 


1-70106 


70446 


70787 


71129 


71473 


71817 


72163 


72509 


72857 


73205 


30 


115 


229 


1-77110 


77471 


77834 


78198 


78563 


78929 


79296 


79665 


80034 


80405 


29 


122 


243 


1-84561 


81946 


85333 


85720 


86109 


86499 


86891 


87283 


87677 


88073 


28 


130 


259 


1-92508 


92920 


93332 


93746 


94162 


94579 


94997 


95417 


95838 


96261 


27 


139 


277 


2-01008 


01449 


01891 


02335 


02780 


03227 


03675 


04125 


04577 


05030 


26 


148 


297 


2-10126 


10600 


11075 


11552 


12030 


12511 


12993 


13477 


13963 


14451 


25 


159 


318 


2-19938 


20449 


20961 


21475 


21992 


22510 


23030 


23553 


2-1077 


24604 


24 


172 


345 


2-30534 


31086 


31641 


32197 


32756 


33317 


33881 


34447 


35015 


35585 


23 


180 


373 


2-42019 


42618 


43220 


43825 


44433 


45043 


45655 


46270 


46888 


47509 


22 


203 


405 


2-54516 


55170 


55827 


56487 


57150 


57815 


58484 


59156 


59831 


60509 


21 






2-68175 


68892 


69612 


70335 


71062 


71792 


72626 


73263 


74004 


74748 


20 






2-83176 


83965 


84758 


85555 


86356 


87161 


87970 


88783 


89GOO 


90421 


19 






2-99738 


oocil 


01489 


02372 


032GO 


04152 


0~5049 


05950 


06867 


07708 


18 






3-18127 


19100 


20079 


21063 


22053 


23048 


24049 


25055 


26067 


27085 


17 






3-38679 


39771 


40869 


41973 


43084 


44202 


45327 


46458 


47596 


48741 


16 






3*61814 


63048 


64289 


65538 


66796 


68061 


69335 


70616 


71907 


73205 


15 






3-88068 


89474 


90890 


92316 


93751 


95196 


96G51 


98117 


99592 


01078 


14 






4-18137 


19756 


21387 


23030 


24684 


26362 


28032 


29724 


31430 


33148 


13 






4-52941 


54826 


56726 


58641 


60572 


62518 


64480 


66458 


68452 


70463 


12 






4-93721 


95945 


98188 


00451 


02734 


05037 


07360 


09704 


12069 


14455 


11 






5-42192 


44857 


47548 


50264 


53007 


55777 


58573 


61397 


64248 


67128 


10 






6-00797 


04051 


07340 


10664 


14023 


17419 


20851 


24321 


27829 


31376 


9 






6-73133 


77199 


81312 


85475 


89688 


93952 


98268 


02637 


07059 


11537 


8 






7-64732 


69957 


75254 


80622 


86064 


91582 


97176 


02848 


08600 


14435 


7 






8-84551 


91520 


98598 


05789 


13093 


20516 


28058 


35724 


43M5 


51436 


6 






10-481 


10-579 


10-678 


10-780 


10-883 


10-988 


11-095 


11-205 


11-316 


11-430 


5 






12-850 


12-596 


13-146 


13-300 


13-457 


13-617 


13-782 


13-951 


14-124 


14-301 


4 






16-587 


16-832 


17'084 


17-343 


17-611 


17-886 


18-171 


18-464 


18-768 


19-081 


3 






23'372 


23-859 


24-368 


24-898 


25-452 


26-031 


26-637 


27-271 


27-937 


28-636 


2 






39-506 


40-917 


42-433 


44-066 


45-829 


47-740 


49-816 


52-081 


54-561 


57-290 


1 






127-32 


143-24 


163-70 


190-98 


229-18 


286-48 


381-97 


572-96 


1145-9 


Inf. 









27' 


24' 


21' 


18' 


15' 


12' 


9' 


6' 


3' 


0' 





r 


2' 


MEA.V 


COTANGENTS, DOT. 



XIII. -NATURAL 



MEAN 


DIFF. 





0' 


3' 


6' 


9' 


12' 


15' 


18' 


2! 


24' 


27* 


30' 


r 


2' 





00000 


00000 


00000 


00000 


00001 


00001 


00001 


00002 


00002 


00003 


00004 








1 


1-00015 


00017 


00018 


00020 


00022 


00024 


00026 


00028 


00030 


00032 


00034 


1 


i 


2 


1-00061 


00064 


00067 


00070 


00074 


00077 


00081 


00084 


00088 


00091 


00095 


1 


8 


3 


1-00137 


00142 


00147 


00151 


00156 


00161 


00166 


00171 


00176 


00182 


00187 


2 


8 


4 


1-00244 


00250 


00257 


00263 


00269 


00276 


00282 


00289 


00296 


00302 


00309 


2 


4 


5 


1-00382 


00390 


00397 


00405 


00413 


00421 


00429 


00438 


00446 


00454 


00463 


3 


5 


6 


1-00551 


00560 


00569 


00579 


00588 


00598 


00608 


00617 


00627 


00637 


00647 


3 


6 


7 


1-00751 


00762 


00773 


00784 


00795 


00806 


00817 


00828 


00840 


00851 


00863 


4 


7 


8 


1-00983 


00995 


01008 


01020 


01033 


01046 


01059 


01071 


01084 


01097 


01111 


4 


9 


9 


1-01247 


01261 


01275 


01289 


01303 


01317 


01332 


01346 


01361 


01376 


01391 


5 


9 


10 


1-01543 


01558 


01574 


01590 


01606 


01622 


01638 


01654 


01670 


01687 


01703 


5 


11 


11 


1-01872 


01889 


01906 


01924 


01941 


01959 


01977 


01995 


02013 


02031 


02049 


6 


11 


12 


1-02234 


02253 


02272 


02291 


02311 


02330 


02349 


02369 


02388 


02408 


02428 


6 


13 


13 


1-02630 


02651 


02672 


02693 


02714 


02735 


02756 


02777 


02799 


02820 


02842 


7 


14 


14 


1-03061 


03084 


0310G 


03129 


03152 


03175 


03197 


03220 


03244 


03267 


03290 


8 


15 


15 


1 -03528 


03552 


03576 


03601 


03625 


03650 


03674 


03699 


03724 


03749 


03774 


8 


17 


16 


1-04030 


04056 


040H2 


04108 


04135 


04161 


04188 


04214 


04241 


04268 


04296 


9 


18 


17 


1-045(5!) 


04597 


04625 


04653 


04682 


04710 


04738 


04767 


04796 


04824 


04853 


10 


19 


18 


1-05146 


05176 


05206 


05236 


05266 


05297 


05327 


05357 


05388 


05418 


05449 


10 


20 


19 


1-05762 


05794 


05826 


05858 


05890 


05922 


05955 


05987 


06020 


06052 


06085 


11 


21 


20 


1-06418 


06452 


06486 


06520 


06554 


06588 


06622 


06657 


06691 


06726 


06761 


11 


23 


21 


1-07114 


07150 


071 86 


07223 


07259 


07295 


07332 


07368 


07405 


07442 


07479 


12 


24 


22 


1-07853 


07892 


07930 


07968 


08006 


08045 


08084 


08122 


08161 


08200 


08239 


13 


26 


23 


1 -08630 


08676 


08717 


08757 


08798 


08839 


08880 


08920 


08962 


09003 


09044 


14 


27 


24 


1-09464 


09506 


09549 


09592 


09635 


09678 


09721 


09764 


09808 


09851 


09895 


14 


29 


25 


1-10338 


10383 


10428 


10473 


10518 


10564 


10609 


10655 


10701 


10747 


10793 


15 


31 


26 


1-11260 


11308 


11355 


11403 


11451 


11499 


11547 


11595 


11643 


11691 


11740 


16 


32 


27 


1-12233 


12283 


12333 


12383 


12433 


12484 


12534 


12585 


12636 


12687 


12738 


17 


34 


28 


1-13257 


13310 


13362 


13415 


13468 


13521 


13575 


13628 


13682 


13735 


13789 


18 


36 


29 


1-14335 


14391 


14446 


14502 


14558 


14614 


14670 


14726 


14782 


14839 


14896 


19 


37 


30 


1-15470 


15528 


15587 


15645 


15704 


15763 


15822 


15881 


15940 


16000 


16059 


20 


39 


31 


1-16663 


16725 


16786 


16848 


16909 


16971 


17033 


17095 


17158 


17220 


17283 


21 


41 


32 


1-17918 


17982 


18047 


18111 


18176 


18241 


18307 


18372 


18437 


18503 


18569 


22 


43 


33 


1-19236 


19304 


19372 


19440 


19508 


19576 


19645 


19713 


19782 


19851 


19920 


23 


45 


34 


1-20622 


20693 


20764 


20836 


20907 


20979 


21051 


21123 


21195 


21268 


21341 


24 


48 


35 


1-22077 


22152 


22227 


22302 


22377 


22453 


22528 


22604 


22680 


22756 


22833 


25 


51 


36 


1-23607 


23685 


23764 


23843 


23922 


24001 


24081 


24160 


24240 


24320 


24400 


2G 


53 


37 


1-25214 


25296 


25379 


25462 


25545 


25628 


25711 


25795 


25879 


25963 


26047 


28 


55 


38 


1-26902 


26988 


27075 


27162 


27250 


27337 


27425 


27513 


27601 


27689 


27778 


29 


68 


39 


1-28676 


28767 


28858 


28950 


29042 


39133 


29226 


29318 


29411 


29504 


29697 


30 


61 


40 


1-80541 


30636 


80732 


30829 


30925 


81022 


31119 


81216 


81313 


81411 


31509 


32 


65 


41 


1-32501 


32602 


32703 


82804 


32905 


83007 


33109 


33211 


33314 


83416 


83519 


34 


68 


42 


1-34563 


34669 


34776 


84882 


34988 


35095 


35203 


35310 


85418 


85526 


35634 


36 


71 


43 


1-36733 


36844 


36956 


37068 


87180 


87293 


37406 


37519 


37632 


37746 


37860 


38 


75 


44 


1-39016 


39134 


39251 


39369 


89487 


39606 


39725 


89844 


39963 


40083 


40203 


40 


79 





60' 


57' | 54' 


61' 


48' 


45' 


42' 


39' 


36' 


33' 


3(X 


r 


2' 


MEAN 


NATURAL Dirr. 



SECANTS. 



MEAN 


DlFF. 


88' 


36* 


30* 


42' 


45' 


48' 


51' 


54' 


67' 


60' 





1' 


2 1 


1-00005 


00005 


00006 


00007 


00009 


00010 


00011 


00012 


00014 


00015 


89 





i 


1-00037 


00039 


00041 


00044 


00047 


00049 


00052 


00055 


00058 


OU061 


88 


1 


2 


1-00099 


00103 


00107 


00111 


00115 


00120 


00124 


00128 


00133 


00137 


87 


1 


3 


1-00192 


00198 


00203 


00209 


00215 


00220 


0022U 


00232 


00238 


00244 


86 


2 


4 


1-00316 


00323 


00330 


00337 


00345 


00352 


00359 


00367 


00374 


00382 


85 


3 


5 


1-00471 


00480 


00488 


00497 


00506 


00515 


00524 


00533 


00542 


00551 


84 


3 


6 


1-00657 


006<>7 


00677 


00688 


00698 


00708 


00719 


00730 


00740 


00751 


83 


3 


7 


1-00875 


00886 


00898 


00910 


00922 


00934 


00946 


00958 


00970 


00983 


82 


4 


8 


1-01124 


01137 


01151 


01164 


01178 


01191 


01205 


01219 


012.J3 


01247 


81 


5 


9 


1-01405 


01420 


01435 


01450 


01466 


01481 


0149G 


01512 


01527 


01543 


80 


5 


10 


1-01720 


01736 


01753 


01769 


01786 


01803 


01820 


01837 


01854 


01872 


79 


6 


11 


1-02067 


02085 


02103 


02122 


02140 


02159 


02178 


02196 


02215 


02234 


78 


6 


12 


1-02448 


02-168 


02488 


02508 


02528 


02548 


02569 


02589 


02UIO 


02030 


77 


7 


13 


1-02863 


02885 


02907 


02928 


02950 


02972 


02994 


03017 


03039 


03061 


76 


7 


15 


1-03313 


03337 


033CO 


03384 


03408 


03432 


03455 


03479 


03503 


03528 


75 


8 


16 


1-03799 


03825 


03850 


03875 


03901 


03927 


03952 


03978 


04001 


01030 


74 


9 


17 


1-04322 


04349 


04376 


04403 


04431 


04458 


04486 


04514 


04541 


04509 


73 


9 


19 


1-04882 


04911 


04940 


04969 


04998 


05028 


05057 


05087 


05116 


05146 


72 


10 


20 


1-05480 


05511 


05542 


05573 


05604 


05636 


05667 


05699 


05730 


05762 


71 


10 


21 


1-06118 


06151 


06181 


06217 


06250 


OG'283 


06317 


06350 


06384 


06418 


70 


11 


22 


1-06796 


06831 


06866 


06901 


06936 


06972 


07007 


07013 


07079 


07114 


69 


12 


23 


1-07516 


07553 


0751)0 


07027 


07665 


07702 


07740 


07778 


07H16 


07853 


68 


U 


25 


1-08278 


08318 


08357 


08397 


08436 


08476 


08516 


08556 


08596 


08030 


67 


13 


26 


1-09086 


09127 


09169 


09211 


09252 


09291 


09337 


09.179 


09421 


O'401 


66 


14 


27 


1-09939 


09982 


10026 


10071 


10115 


10159 


10204 


10248 


10293 


10338 


65 


15 


29 


1-10839 


10885 


10932 


10978 


11025 


11072 


11119 


11166 


11213 


11260 


64 


16 


31 


1-11789 


11838 


11886 


11936 


11985 


12034 


12083 


12133 


12183 


12233 


63 


16 


33 


1-12789 


12841 


12892 


12944 


12996 


13048 


13100 


13152 


13205 


1.T257 


62 


17 


35 


1-13843 


1381)7 


13952 


14006 


14061 


14115 


14170 


14225 


14280 


14335 


61 


18 


87 


1-14952 


15009 


15066 


15124 


15181 


15239 


15296 


15354 


15412 


15470 


60 


19 


88 


1-16119 


16179 


16239 


16299 


16359 


16420 


16481 


16541 


16602 


16663 


59 


20 


40 


1-17346 


17409 


17472 


17635 


17598 


17662 


17726 


17790 


17853 


17918 


58 


21 


42 


1-18635 


18701 


18767 


18834 


18901 


18967 


19034 


19102 


19109 


19236 


57 


22 


45 


1-19990 


20059 


20129 


20199 


20269 


20339 


20410 


20480 


20551 


20022 


56 


23 


47 


1-214H 


21487 


21560 


21633 


21707 


21781 


21855 


21929 


22003 


22077 


55 


25 


49 


1-22909 


22986 


23063 


23140 


23217 


23296 


23373 


23450 


23529 


23607 


54 


26 


5L 


1-24181 


24561 


24642 


24723 


24804 


24886 


24967 


25049 


25131 


25214 


53 


27 


54 


1-26132 


26216 


26301 


26387 


26472 


26557 


26643 


26729 


26815 


26902 


52 


28 


57 


1-27867 


27956 


28045 


28184 


28224 


28314 


28404 


28495 


28585 


28076 


61 


30 


60 


1-29690 


29784 


29877 


29971 


30066 


30160 


30255 


30350 


30445 


30541 


50 


31 


63 


1-31607 


31705 


31804 


31903 


32002 


32101 


32201 


32301 


32401 


32501 


49 


33 


66 


1-33622 


33726 


33830 


33934 


34038 


34142 


34247 


34352 


34458 


31563 


48 


35 


69 


1-35743 


35852 


359G1 


36070 


36180 


36290 


36400 


36511 


36622 


30733 


47 


37 


73 


1-37974 


38089 


38204 


38319 


38434 


38550 


38C66 


38783 


38899 


89016 


46 


88 


77 


1-40324 


40444 


40565 


40687 


4080S 


40930 


41053 


41175 


41298 


414-21 


45 


40 


81 


27' 


24' 


21' 


18' 


15' 


12' 


& 


6' 


3' 


<y 





r 


2' 


MEAN 


COSECANTS. Dur. 



NATURAL 



MEAN 


DIFF. 





a 


3' 


8' 


9' 


12' 


15' 


18' 


21' 


24' 


2T 


3<X 


r 


2' 


45 


1-41421 


41546 


41669 


41793 


41918 


42042 


42168 


42293 


42419 


42545 


42672 


41 


83 


46 


1-43056 


44086 


44217 


44347 


44479 


44610 


44742 


44875 


45007 


45141 


45274 


43 


87 


47 


1*46628 


467(55 


46903 


47041 


47180 


47319 


47458 


47598 


47738 


47878 


48019 


46 


93 


48 


1-49148 


40593 


49738 


49884 


50030 


50177 


50324 


50471 


50619 


50767 


50916 


49 


98 


49 


1-52425 


62579 


52782 


52886 


53041 


53196 


63351 


53507 


53663 


53820 


53977 


52 


103 


60 


1-55572 


55734 


55897 


56060 


56223 


56387 


56551 


56716 


56881 


57047 


57213 


55 


109 


61 


1-58!)02 


59073 


59245 


59418 


59590 


69764 


59938 


60112 


60287 


60463 


60639 


58 


116 


62 


1-62427 


G2609 


(52791 


(52971 


63157 


63341 


63525 


63710 


63895 


64081 


64268 


61 


123 


63 


1-66164 


C6357 


66:>60 


60744 


60038 


67133 


67329 


67525 


67722 


67919 


68117 


(55 


130 


64 


1-70130 


70335 


70540 


70746 


70H53 


71160 


71368 


71576 


71785 


71995 


72205 


69 


138 


66 


1-74345 


74562 


74781 


75000 


75219 


75440 


75661 


75882 


76105 


76328 


76552 


74 


147 


66 


1-78829 


79061 


79293 


79527 


79761 


79995 


80231 


80467 


80704 


80942 


81180 


78 


15G 


57 


1-8360H 


83855 


84103 


84352 


84(101 


84852 


85103 


85355 


85608 


85861 


86116 


83 


167 


58 


1-88708 


88972 


8<J237 


89503 


89769 


90037 


90305 


90375 


90815 


91116 


91388 


89 


179 ( 


59 


1-941CO 


94413 


94726 


95011 


95296 


95583 


95870 


96158 


96448 


96738 


97029 


96 


191 


60 


2-00000 


00303 


00607 


00912 


01218 


01525 


01833 


02143 


02153 


02765 


03077 


102 


205 


61 


2-0'.2G7 


06592 


009 18 


07246 


07575 


07905 


08236 


08569 


08903 


09238 


09574 


110 


220 


62 


2-13005 


13356 


13707 


14000 


14414 


14770 


15127 


15485 


15845 


10206 


10568 


119 


237 


68 


2-20209 


20(547 


21 026 


21407 


21790 


22174 


22559 


22946 


23334 


23724 


24116 


128 


256 


64 


2-28117 


28526 


28937 


29349 


29763 


30179 


30596 


31015 


31436 


31858 


32282 


139 


277 


65 


2-36620 


37064 


37509 


37957 


38106 


38857 


39311 


39766 


40222 


40681 


41142 


150 


301 


66 


2-45859 


46342 


46827 


47314 


47804 


48295 


48789 


49284 


49782 


50282 


50784 


164 


327 


67 


2-55930 


56458 


66!)88 


57520 


58054 


5851)1 


59130 


59672 


60217 


60763 


61313 


179 


358 


68 


2-66947 


67525 


68105 


68689 


69275 


69864 


70455 


71050 


71647 


72247 


72850 






69 


2-79043 


79679 


80318 


80960 


81605 


82254 


82906 


83561 


84219 


84880 


85545 






70 


2-92380 


93083 


93790 


94500 


95213 


95931 


9GG52 


97377 


98106 


98838 


99574 






71 


3-07155 


07930 


OH721 


09510 


10303 


11101 


11903 


12709 


13520 


14335 


15155 






72 


8-23607 


24478 


25355 


2(5237 


27123 


28015 


28912 


29814 


30721 


31(533 


32551 






73 


3-42030 


43010 


43995 


44986 


45983 


46986 


47995 


49010 


50032 


510GO 


52094 






74 


3-62796 


63903 


65018 


66140 


67269 


68405 


69549 


70700 


71858 


73024 


74198 






75 


3-86370 


87633 


88904 


90184 


91473 


92770 


94076 


95392 


96716 


98050 


99393 






78 


4-13357 


14809 


16271 


17744 


19228 


20723 


22229 


23746 


25275 


26814 


28366 






77 


4-44341 


46228 


47928 


49G42 


51368 


53109 


548G3 


5G632 


58414 


60211 


62023 






78 


4-80973 


82956 


84956 


86973 


89007 


91058 


93128 


95215 


97320 


99443 


01585 






79 


5-24084 


20448 


28833 


31241 


33671 


36124 


38600 


41099 


43622 


46169 


48740 






80 


5-75877 


78742 


81635 


84558 


87511 


90495 


93509 


96555 


99633 


02743 


05886 






81 


6-39245 


42787 


46369 


49991 


53655 


57361 


61110 


64902 


68738 


72620 


76547 






82 


7-18530 


23019 


27566 


32171 


36835 


41560 


46346 


51194 


56107 


61085 


66130 






83 


8-20551 


26425 


32384 


38431 


44566 


50793 


57113 


63528 


70041 


76653 


83367 






84 


9'5fi677 


64687 


72833 


81119 


89547 


98123 


10-068 


10-157 


10-248 


10-340 


10-433 






85 


11-474 


11-589 


11-707 


11-828 


11-951 


12-076 


12-204 


12-335 


12-469 


12-606 


12-745 






86 


14-836 


14-517 


14-703 


14-893 


15-089 


15-290 


15-496 


15-708 


15-926 


16-150 


16-380 






87 


19-107 


19-431 


19-766 


20-112 


20-471 


20-843 


21-229 


21-629 


22-044 


22-476 


22-926 






88 


28-654 


29-388 


30-161 


30-976 


31-836 


32-746 


33-708 


84-730 


35-815 


36-970 


38-202 






89 


57-299 


60-314 


63-665 


67-409 


71-622 


76-397 


81-853 


88-149 


96-495 


104-18 


114-59 









60' 


57' 


64' 


61' 


48' 


45' 


42' 


39' 


36' 


33' 


80' 


r 


2' 


MEAN 


NATURAL Dirr. 



4j 



MKAH' 


DlFF. 


83' 


36' 


39' 


42' 


45' 


48' 


61' 


54' 


57' 


60' 





r 


2' 


1-42799 


42926 


43053 


43181 


43310 


43438 


43567 


43696 


43826 


43956 


44 


43 


86 


1-45408 


45542 


45676 


45811 


45946 


46082 


46218 


46354 


46491 


46628 


43 


45 


90 


1-48160 


48301 


48443 


48586 


48728 


48871 


49015 


49159 


49303 


49448 


42 


47 


95 


1-51065 


51215 


51364 


51515 


51665 


51817 


51968 


52120 


52273 


62425 


41 


50 


100 


1-54134 


54292 


64451 


54610 


64769 


64929 


55089 


65250 


65411 


55572 


40 


53 


106 


1-57380 


57547 


57715 


57883 


58051 


58221 


58390 


58560 


58731 


58902 


39 


56 


112 


1-60815 


60992 


61170 


61348 


61526 


61705 


61885 


62065 


62246 


62427 


38 


69 


119 


1-64455 


64643 


64831 


65020 


65209 


65399 


65589 


65780 


C5972 


66164 


37 


63 


1'26 


1-68316 


68515 


68715 


68915 


69116 


60318 


69520 


69723 


69926 


70130 


36 


67 


134 


1-72416 


72628 


72840 


73053 


73267 


73481 


73696 


73911 


74128 


74345 


35 


71 


143 


1-76776 


77001 


77227 


77454 


77681 


77910 


78138 


78368 


78598 


78829 


34 


76 


151 


1-81419 


81 659 


81900 


82142 


82384 


82627 


82871 


83116 


83362 


83G08 


33 


81 


161 


1-86371 


86627 


86885 


87142 


87401 


87661 


87921 


88183 


88445 


88708 


32 


86 


173 


1-91661 


911)35 


92210 


92486 


92762 


93040 


93319 


93508 


93879 


941 GO 


31 


92 


187 


1-97322 


97615 


97910 


98205 


98502 


98799 


99098 


99398 


99698 


00000 


30 


99 


198 


2-03391 


03706 


04022 


04.339 


04657 


04977 


05298 


05619 


05942 


06267 


29 


106 


213 


2-09911 


10250 


10590 


10931 


11274 


11617 


11963 


12301) 


12657 


i:u)o;> 


28 


114 


232 


2-16932 


17297 


17663 


18031 


18401 


18772 


19144 


UU7 


1981)2 


202G1) 


27 


123 


247 


2-24509 


24003 


25.'M)0 


23697 


26097 


26498 


26900 


27304 


27710 


28117 


26 


133 


2G7 


2-32708 


33135 


33565 


33996 


34429 


34863 


35300 


35738 


36178 


36620 


25 


114 


289 


2-41605 


42070 


42536 


43005 


43476 


43948 


44423 


44900 


45378 


45859 


24 


157 


314 


2'51289 


51795 


52304 


52815 


53329 


53845 


513G3 


51883 


55405 


551)30 


23 


171 


313 


2'61864 


62410 


62976 


63535 


64097 


01662 


65229 


65799 


6(1371 


661)47 


22 


187 


376 


2-73456 


74065 


74(577 


75292 


75909 


76530 


77154 


77780 


78110 


71)043 


21 






2-86213 


86885 


87560 


88238 


88920 


81)605 


90293 


90986 


91681 


92380 


20 






8-00315 


01059 


01807 


02559 


03315 


04075 


04839 


05607 


06379 


07155 


19 






8-15979 


16808 


17641 


18479 


19322 


201G9 


21021 


21878 


22740 


2JJ607 


18 






S'33474 


34403 


35336 


3(i276 


37221 


38171 


31)128 


40089 


41057 


42030 


17 






S'53134 


54181 


55234 


56294 


57361 


68434 


61)514 


60601 


616D5 


6279G 


16 






3-75379 


76568 


77765 


781)70 


80183 


81404 


82633 


83871 


85116 


86370 


15 






4-00745 


02107 


03479 


04860 


06251 


07652 


09063 


10484 


11915 


13357 


14 






4'29929 


31503 


33090 


34689 


36299 


37923 


39558 


41206 


428G7 


44541 


13 






4-63849 


65690 


67545 


69417 


71303 


73205 


75123 


77057 


71)007 


801)73 


12 






5-03746 


051)26 


08125 


10344 


12583 


14842 


17121 


19421 


21742 


24084 


11 






5-51337 


53958 


56605 


69277 


61976 


64701 


67454 


70234 


73041 


75877 


10 






6-09062 


12273 


15517 


18797 


22113 


25464 


28853 


32279 


35743 


39245 


9 






6-80521 


84542 


88612 


92731 


90900 


OTI20 


05392 


"09717 


T4096 


18530 


8 






7-71242 


76424 


81677 


87001 


92399 


97873 


03423 


09052 


14760 


20551 


7 






8-90186 


97111 


04146 


H292 


18553 


25931 


33430 


41052 


48800 


56677 


6 






10-529 


10-626 


10-725 


10-826 


10-929 


11-034 


11-140 


11-249 


11-360 


11-474 


5 






12-888 


13-u35 


13-184 


13-337 


13-494 


13-654 


13-818 


13-987 


14-159 


14-336 


4 






16-618 


16-862 


17-113 


17-372 


17-639 


17-914 


18-198 


18-492 


18-794 


19-107 


3 






23-393 


23-880 


24-388 


24-918 


25-471 


26-050 


26-655 


27-290 


27-955 


28-654 


2 






89-519 


40-930 


42-445 


44-077 


45-840 


47-750 


49-826 


52-090 


54-570 


57-299 


1 






127-33 


143-24 


163-70 


190-99 


229-18 


286-48 


381-97 


672-96 


1145-9 


Inf. 









27' 


24' 


21' 


18' 


15' 


12' 


& 


& 


3' 


<y 





r 


2' 

i 


MEAN 


COSECANTS. DIFF. 



44 



XIV.-LOaARITHMIC 



MEAN 


Dirr. 





O 1 


3' 


6' 


9' 


12' 


15' 


18' 


21' 


24' 


2T 


30' 


r 


2' 





Inf. Neg. 


6-94085 


7-24188 


41797 


54291 


63982 


71900 


78594 


84393 


89509 


94084 






1 


8-24186 


26301 


28324 


30255 


32103 


33875 


35578 


37217 


38796 


40320 


41792 






2 


8-54282 


55354 


50400 


57421 


58419 


59395 


60349 


61282 


62196 


63091 


63968 






3 


8-71880 


72597 


73303 


73997 


74680 


75353 


76015 


76667 


77310 


77943 


78568 






4 


8-84358 


84897 


85429 


85955 


80474 


86987 


87494 


87995 


88490 


88980 


89464 


170 


339 


5 


8-940.10 


94461 


94887 


95310 


95728 


96143 


96553 


96960 


97363 


97762 


98157 


137 


275 


6 


9-01923 


02283 


02(539 


02992 


03342 


03690 


04034 


04376 


04715 


05052 


05386 


115 


230 


7 


9 08589 


08897 


09202 


09506 


09807 


10106 


10402 


10697 


10990 


11281 


11570 


99 


198 


8 


9-14:556 


14024 


14891 


15157 


15421 


15683 


15944 


16203 


16460 


16716 


16970 


87 


174 


e 


9-19433 


19072 


19909 


20145 


20380 


20613 


20845 


21076 


21306 


21534 


21761 


78 


155 


10 


9-23967 


24181 


24395 


24607 


24818 


25028 


25237 


25445 


25052 


25858 


26063 


70 


140 


11 


9-28060 


28254 


28448 


28641 


28833 


29024 


29214 


29403 


2D591 


29779 


29966 


63 


127 


12 


9-31788 


31966 


32143 


32319 


324!15 


32670 


32844 


33018 


33190 


33362 


33534 


58 


116 


13 


9-85209 


35373 


35536 


35698 


35860 


36022 


36182 


36312 


36502 


36660 


36819 


54 


107 


14 


9-38368 


38519 


38670 


38821 


38971 


39121 


39270 


39418 


39566 


39713 


39860 


60 


99 


15 


9-41300 


41441 


41582 


41722 


41861 


42001 


42140 


42278 


42416 


42553 


42690 


46 


93 


16 


9-44034 


44106 


44-297 


44428 


4-1559 


44689 


44819 


44948 


45077 


45206 


45334 


43 


87 


17 


9-46594 


40717 


46841 


46964 


47086 


47209 


47330 


47452 


47573 


47694 


47814 


41 


81 


18 


9-48998 


49115 


49231 


49317 


49462 


49577 


49692 


49806 


49920 


50031 


50148 


38 


77 


10 


9-512G4 


51374 


51484 


51593 


51702 


61811 


51919 


52027 


52135 


62242 


62350 


36 


72 


20 


9-53405 


53509 


53613 


53716 


53819 


53922 


54025 


54127 


54229 


54331 


54433 


34 


68 


21 


9-55433 


55532 


55630 


55728 


55826 


55923 


66021 


56118 


56215 


56311 


66408 


32 


65 


22 


9-57358 


57451 


57545 


57638 


57731 


57824 


67916 


58008 


58101 


58192 


68284 


31 


62 


23 


9-59188 


59277 


59366 


69455 


59543 


59632 


59720 


59808 


59895 


59983 


60070 


29 


59 


24 


9-60931 


61016 


61101 


61186 


61270 


61354 


61438 


61522 


61606 


61689 


61773 


28 


56 


25 


9-62595 


62676 


62757 


62838 


62918 


62999 


63079 


63159 


63239 


63319 


63398 


27 


54 


26 


9-64181 


G4 26 2 


64339 


64417 


64 194 


64571 


64647 


64724 


64800 


64877 


64953 


26 


51 


27 


9-65705 


65779 


65853 


65927 


6(5001 


66075 


66148 


66221 


61.295 


66368 


66441 


25 


49 


28 


9-67101 


67232 


67303 


67374 


67445 


67515 


67586 


67656 


67726 


67796 


67866 


24 


47 


29 


9-68557 


68625 


68694 


68762 


68829 


68897 


68965 


69032 


69100 


69167 


69234 


23 


45 


30 


9-69897 


69963 


70028 


70093 


70159 


70224 


70288 


70353 


70418 


70482 


70547 


22 


43 


31 


9-71181 


71247 


71310 


71373 


71435 


71498 


71560 


71622 


71685 


71747 


71809 


21 


42 


32 


9-72421 


72182 


72542 


72602 


72663 


72723 


72783 


72843 


72902 


72962 


73022 


20 


40 


33 


9-73611 


7306!) 


73727 


73785 


73843 


73901 


73959 


74017 


74074 


74132 


74189 


19 


39 


34 


9-74756 


74812 


748158 


74924 


74980 


75036 


75091 


75147 


75202 


75258 


75313 


19 


38 


35 


9-75859 


75913 


75967 


76021 


76075 


76129 


76182 


76236 


76289 


76342 


76395 


18 


36 


36 


9-7G922 


76974 


7702li 


77078 


77130 


77181 


77233 


77285 


77336 


77387 


77439 


17 


34 


37 


9-7794IJ 


77997 


78047 


78097 


78147 


78197 


78246 


78296 


78346 


78395 


78445 


17 


33 


38 


9-78934 


78983 


79031 


79079 


79128 


79176 


79224 


79272 


79319 


79367 


79415 


16 


32 


39 


9-79887 


79934 


79981 


80027 


80074 


80120 


80166 


80213 


80259 


80305 


80351 


15 


31 


40 


9-80807 


80852 


80897 


80942 


80987 


81032 


81076 


81121 


81166 


81210 


81251 


15 


30 


41 


9-81694 


81738 


81781 


81825 


818i)8 


81911 


81955 


81998 


82041 


8208 1 


82126 


14 


29 


42 


9-82551 


82593 


82635 


82677 


82719 


827il 


82802 


82844 


82885 


82927 


82968 


14 


28 


43 


9-83378 


83419 


83459 


83500 


83540 


83581 


83621 


83661 


8370 1 


83711 


83781 


13 


27 


44 


9-84177 


84216 


84255 


84295 


84334 


84373 


84411 


84450 


84489 


81528 


84566 


13 


26 





60' 


67 


54' 


51' 


48' 


45' 


42' 


39' 


36' 


QQf 
OO 


30' 


1' 


2 


MEAN 


LOGARITHMIC DOT. 



45 



SINES. 



MEAN 


DIFF, 


33' 


36' 


39' 


42' 


45' 


48' 


51' 


54' 


57' 


60' 





r 


2' 


7'98223 




05478 






14495 


17123 




21958 




89 






02002 


08696 


11693 


19610 


24180 


8-43216 


44594 


45930 


47226 


48485 


49708 


50897 


62055 


63183 


54282 


88 






8-64827 


65670 


66197 


67308 


68104 


68886 


69654 


70409 


71151 


71880 


87 






8-7!'183 


79789 


80388 


80978 


81560 


82134 


82701 


83201 


83813 


84358 


86 






8-89943 


90417 


90885 


91349 


91807 


92261 


92710 


93154 


93594 


94030 


85 


152 


303 


8-98549 
9-05717 


98937 
06046 


99322 
00372 


99704 
00696 


00082 
07018 


00456 
07337 


00828 
07653 


01106 
07068 


01501 
08280 


OT923 

08589 


84 
83 


125 
107 


251 
213 


9-11857 


12142 


12425 


12706 


12085 


13203 


13539 


13813 


14085 


14356 


82 


03 


185 


9-17223 


17474 


17724 


17973 


18220 


18465 


18709 


18052 


10103 


lit 133 


81 


82 


164 


9-21987 


22211 


22435 


22657 


22878 


23098 


23317 


23535 


23752 


23007 


80 


73 


147 


9-26267 


26470 


26672 


26873 


27073 


27273 


27471 


27668 


27864 


28000 


79 


66 


133 


9*30151 


30336 


30521 


30701 


30H87 


3100S 


31250 


3 14, TO 


31009 


31788 


78 


61 


121 


9-33704 


33874 


34043 


34212 


34380 


34547 


34713 


34879 


35044 


35209 


77 


50 


112 


9-36976 


37133 


37289 


37445 


37000 


37755 


37909 


38002 


38215 


383(58 


76 


52 


103 


9-40006 


40152 


40297 


40442 


40586 


40730 


40873 


41016 


41168 


41300 


75 


48 


96 


9-42826 


42P62 


43098 


43233 


43307 


43502 


43635 


43709 


43001 


44031 


74 


45 


90 


9-45462 


45589 


45716 


45843 


45!)0!) 


40005 


46220 


40345 


40109 


46594 


73 


42 


84 


9-47934 


48054 


48173 


48292 


48411 


4H529 


48047 


48704 


4X881 


48008 


72 


30 


79 


9-50261 


50374 


60486 


50598 


50710 


50821 


50033 


51043 


51154 


51204 


71 


37 


74 


9-52456 


52563 


52069 


52775 


52881 


62986 


63092 


53106 


3301 


53405 


70 


35 


70 


9-54534 


54635 


54735 


54836 


54936 


55036 


55136 


55235 


55331 


55433 


69 


33 


67 


9-56504 


50509 


50095 


50700 


50886 


50080 


57075 


571 CD 


57204 


57358 


68 


32 


03 


9*58375 


58-107 


58557 


58618 


58739 


58829 


58010 


50000 


50008 


61)188 


67 


30 


00 


9-60157 


60244 


60331 


60117 


00503 


60589 


60075 


60701 


60846 


60031 


66 


28 


67 


9-61856 


61939 


62021 


62104 


62186 


62268 


62350 


62132 


62513 


62695 


65 


27 


65 


9-63478 


63557 


63630 


63715 


63794 


63872 


63050 


64028 


64106 


04181 


64 


26 


62 


9-65029 


65101 


05180 


65255 


05331 


65406 


65481 


65556 


(.5030 


05705 


63 


25 


50 


9-60513 


60586 


G0058 


6(5731 


66803 


60875 


G0040 


67018 


67000 


07101 


62 


24 


48 


9-67036 


68006 


G8075 


6H144 


68213 


68283 


08351 


68L'0 


684 80 


68557 


61 


23 


46 


9-69301 


69368 


09431 


60501 


69567 


69633 


69699 


69765 


60831 


69807 


60 


22 


44 


9-70611 


70675 


70739 


70803 


70867 


70931 


70994 


71058 


71121 


71184 


59 


21 


42 


9-71870 


71932 


71994 


72055 


72116 


72177 


72238 


72209 


72300 


7-2421 


58 


20 


40 


9-73081 


7.5140 


73200 


73259 


73318 


73377 


73435 


73404 


73552 


73011 


57 


20 


30 


9-74246 


74303 


74300 


74417 


74474 


74531 


74587 


74044 


74700 


74750 


56 


10 


38 


9-75368 


75423 


75478 


75533 


75587 


75642 


76696 


75751 


75805 


75869 


55 


18 


36 


9-76148 


76501 


76554 


76607 


76660 


76712 


76765 


76817 


76870 


70022 


54 


18 


35 


9-77490 


77541 


77592 


77643 


770') 1 


77744 


77705 


77846 


77806 


77046 


53 


17 


34 


9-78494 


78543 


78592 


78042 


78001 


78739 


78788 


78837 


78886 


78934 


52 


16 


33 


9-79463 


79510 


79553 


79005 


79652 


70699 


79746 


70703 


79840 


79887 


51 


16 


31 


9-80397 


80443 


80489 


80534 


80580 


80625 


80671 


80716 


80762 


80807 


50 


15 


30 


9-81299 


81343 


81387 


81431 


81475 


81519 


81563 


81007 


81651 


81604 


49 


15 


29 


9-82169 


82212 


82255 


82297 


82340 


82382 


824'24 


82167 


82509 


82551 


48 


14 


28 


9-83010 


83051 


83092 


83133 


83174 


83215 


83256 


83297 


83338 


83378 


47 


14 


27 


9-83821 


83861 


83901 


83940 


83980 


84020 


84059 


84098 


84138 


84177 


46 


13 


26 


0-84605 


84643 


84682 


84720 


84758 


84796 


84835 


84873 


84911 


84949 


45 


13 


26 


27' 


24' 


21' 


18' 


15' 


12' 


& 


0' 


3' 


0' 





r 


2' 


MKAN 


COSINES. DIFF. 



4 6 



LOGARITHMIC 



MEAN 


DlFF. 





0' 


3' 


6' 


9' 


12' 


15' 


18' 


21' 


24' 


27' 


3<X 


r 


2' 


45 


9-84949 


84986 


85024 


85062 


85100 


85137 


85175 


85212 


85250 


85287 


85324 


13 


25 


46 


9-85093 


85730 


85766 


85803 


85839 


85876 


85912 


85948 


85984 


86020 


86056 


12 


24 


47 


9-8G413 


86448 


861XJ 


86518 


86554 


86589 


86624 


86659 


86694 


86728 


86763 


12 


23 


48 


9-87107 


87141 


87175 


87209 


87243 


87277 


87311 


87345 


87378 


87412 


87446 


11 


23 


49 


9-87778 


87811 


87844 


87877 


87909 


87942 


87975 


88007 


88040 


88072 


88105 


11 


22 


50 


9-88425 


88457 


8818D 


88520 


88552 


88584 


88615 


88647 


88G78 


88709 


88741 


10 


21 


61 


9-81>0. r >0 


89081 


89112 


89142 


81)173 


89203 


89233 


89264 


89294 


89324 


89354 


10 


20 


52 


9-81Mif>3 


81)683 


81)712 


89742 


89771 


89801 


89830 


89859 


89888 


89918 


89947 


10 


19 


53 


9 '90235 


90263 


902H2 


90320 


90349 


90377 


90405 


90434 


90462 


90490 


90518 


9 


19 


54 


9-90796 


90823 


90851 


90878 


90906 


90933 


90960 


90987 


91014 


91042 


91069 


9 


18 


55 


9-91336 


91363 


913H9 


91416 


91442 


91469 


91495 


91521 


91547 


91573 


91599 


9 


17 


56 


9*91857 


91883 


91908 


1)1934 


91959 


91985 


92010 


92035 


920(10 


92086 


92111 


8 


17 


57 


9- 9235!) 


92381 


92408 


1)2433 


92157 


92482 


92506 


92530 


92555 


92579 


92603 


8 


16 


58 


9-92812 


92866 


1)2889 


921)13 


1)2936 


92960 


92983 


93007 


93030 


93053 


93077 


8 


16 


59 


9- 93307 


93329 


93352 


93375 


93397 


93420 


93442 


93465 


93487 


93510 


93532 


8 


15 


60 


9-93753 


93775 


93797 


93819 


93810 


93862 


93881 


93905 


93927 


93948 


93970 


7 


14 


61 


9-91182 


94203 


94224 


94245 


94V66 


94286 


94307 


94328 


94349 


1)4369 


94390 


7 


14 


62 


9-94593 


94614 


94634 


94654 


94<>74 


94694 


94714 


91731 


1)4753 


94773 


94793 


7 


13 


63 


9-94DHK 


95007 


95027 


95046 


95065 


95084 


95103 


95122 


95141 


95160 


95179 


6 


13 


64 


9-1)5366 


95384 


95403 


95421 


95440 


95458 


95476 


95494 


95513 


95531 


95549 


6 


12 


65 


9-95728 


95745 


95763 


1)5780 


95798 


95815 


95833 


95850 


95868 


95885 


95902 





12 


66 


9-96073 


96090 


%107 


96123 


96140 


96157 


96174 


96190 


96207 


1)6223 


96240 


6 


11 


67 


9-96103 


96419 


H6135 


96451 


1)6467 


96483 


1)6498 


96514 


96530 


1)65-16 


1)6562 


5 


11 


68 


9-96717 


96732 


96747 


1)6762 


96778 


96793 


96808 


96823 


96838 


96853 


96868 


5 


10 


69 


9-97015 


97030 


97044 


97059 


97073 


97087 


97102 


97116 


97130 


97145 


97159 


5 


10 


70 


9-97299 


97312 


97326 


97340 


97353 


97367 


97381 


97394 


97408 


97421 


97435 


5 


9 


71 


9-97567 


97580 


9751)3 


97606 


97619 


97632 


97645 


97657 


97670 


97683 


97696 


4 


9 


72 


9-97821 


97833 


97815 


1)7857 


97870 


97882 


97894 


97906 


97918 


97930 


97942 


4 


8 


73 


9-98060 


98071 


98083 


9809 1 


98106 


98117 


98129 


98140 


98151 


98162 


98174 


4 


8 


74 


9-98284 


98295 


98306 


98317 


98327 


98338 


98349 


98359 


98370 


98381 


98391 


4 


7 


75 


9-98494 


98505 


98515 


98525 


98535 


98545 


98555 


98565 


98574 


98584 


98594 


3 


7 


76 


9-98690 


98700 


98709 


1KH711) 


98728 


98737 


98746 


98756 


98765 


98774 


98783 


3 


6 


77 


9-98872 


98881 


DK890 


988D8 


98907 


98916 


98924 


98933 


98941 


98950 


98958 


3 


6 


78 


9-99040 


99048 


99056 


9906 1 


99072 


99080 


99088 


99096 


91)104 


99112 


99119 


3 


5 


79 


9-99195 


99202 


99209 


99217 


99224 


99231 


99238 


99245 


99252 


99260 


99267 


2 


6 


80 


9-99335 


99342 


99348 


99355 


99362 


99368 


99375 


99381 


99388 


99394 


99400 


2 


4 


81 


9-99162 


99468 


1)9474 


1)1)480 


90486 


99492 


99497 


99503 


99509 


99515 


99520 


2 


4 


82 


9-99575 


99581 


99586 


995D1 


99596 


99601 


99607 


99612 


99617 


99622 


99627 


2 


3 


83 


9-99675 


99680 


9968 1 


99689 


99693 


99698 


99702 


99707 


99711 


99716 


99720 


2 


3 


84 


9-99761 


997<>5 


99769 


99773 


99777 


99781 


99785 


99788 


99792 


99796 


99800 


1 


3 


85 


9-99834 


99838 


99841 


99844 


99847 


99851 


99854 


99857 


99860 


998G3 


99866 


1 


2 


86 


9-99894 


90897 


99899 


991)02 


99904 


99907 


99909 


99912 


99914 


99917 


99919 


1 


2 


87 


9-99940 


99912 


99944 


99946 


99948 


99950 


99952 


99954 


99955 


99957 


99959 


1 


1 


88 


9-99974 


99975 


99976 


99977 


99979 


99980 


99981 


99982 


99983 


99984 


99985 





1 


89 


9-99993 


99994 


99995 


99995 


99996 


99996 


99997 


99997 


99998 


99998 


99998 











60' 


57' 


54' 


51' 


48' 


45' 


42' 


39' 


36' 


33' 


30' 


r 


2' 


MEAN 


LOGARITHMIC DIFF. 



47 



SINES continued. 



MEAN 


DlFF. 


33' 


36' 


39' 


42' 


45' 


48' 


61' 


64' 


67' 


60' 


o 


r 


2' 


9-85361 


85399 


85436 


85473 


85510 


85547 


85583 


85620 


85657 


85693 


44 


12 


25 


9-86092 


86128 


86164 


86200 


86235 


86271 


86306 


86342 


86377 


86413 


43 


12 


24 


9-86798 


86832 


86867 


86902 


86936 


86970 


87005 


87039 


87073 


87107 


42 


11 


23 


9-87479 


87513 


87546 


87579 


87613 


87646 


87679 


87712 


87745 


87778 


41 


11 


22 


9-88137 


88169 


88201 


88234 


88266 


88298 


88330 


88362 


88394 


88425 


40 


11 


21 


9-88772 


88803 


88834 


88865 


88896 


88927 


88958 


88989 


89020 


89050 


39 


10 


21 


9-89385 


89415 


89445 


89475 


89504 


89534 


89564 


89594 


89621 


89653 


38 


10 


20 


9-89076 


90005 


90034 


90063 


90091 


90120 


90149 


90178 


90206 


90235 


37 


10 


19 


9-90546 


90574 


90602 


90630 


90657 


90685 


90713 


90741 


90768 


90796 


36 


9 


19 


9-91096 


91123 


91149 


91176 


91203 


91230 


91257 


91283 


91310 


91336 


36 


9 


18 


9-91625 


91651 


91677 


91703 


91729 


91755 


91781 


91806 


91832 


91857 


34 


9 


17 


9-92136 


92161 


92186 


92211 


92235 


92260 


92285 


92310 


92335 


92359 


33 


8 


17 


9-92627 


92651 


92675 


92699 


92723 


92747 


92771 


9275 


92818 


92812 


32 


8 


16 


9-93100 


93123 


93146 


93169 


93192 


93215 


93238 


93261 


93284 


93307 


31 


8 


15 


9-93554 


93577 


93599 


93621 


93643 


936G5 


93687 


93709 


93731 


93753 


30 


7 


15 


9-93991 


94012 


94034 


94055 


94076 


94098 


94119 


94140 


94161 


94182 


29 


7 


14 


9'944 JO 


91431 


94451 


94472 


94492 


94513 


94533 


94553 


94573 


94593 


28 


7 


14 


9-94813 


94832 


94852 


94871 


94891 


91911 


94930 


9494!* 


941)69 


949H8 


27 


7 


13 


9-95198 


95217 


95236 


95254 


95273 


95292 


95310 


95329 


95318 


95361] 


26 


6 


12 


9-95567 


95585 


95603 


95621 


95639 


95657 


95674 


95692 


95710 


95728 


25 


6 


12 


9-95920 


95937 


95954 


95971 


95988 


96005 


96022 


96039 


96056 


96073 


24 


6 


11 


9-96256 


96273 


96289 


9(5305 


96322 


96338 


96354 


96370 


96387 


1)6403 


23 


5 


11 


9-96577 


96593 


96608 


961.24 


96640 


96655 


96670 


96686 


96701 


96717 


22 


5 


10 


9-96883 


96898 


96912 


96927 


96942 


96957 


96971 


961)86 


97001 


97015 


21 


6 


10 


9-97173 


97187 


97201 


97215 


97229 


97213 


97257 


97271 


97285 


97299 


20 


5 


9 


9-97448 


97461 


97475 


97488 


97501 


97515 


97528 


97541 


97554 


97567 


19 


4 


9 


9-97708 


97721 


97734 


97746 


97759 


97771 


97784 


97796 


97808 


97821 


18 


4 


8 


9-97954 


97966 


97978 


97989 


98001 


98013 


98025 


98036 


9H018 


98060 


17 


4 


8 


9-98185 


98196 


98207 


98218 


98229 


98240 


98251 


98262 


98273 


9H284 


16 


4 


7 


9-98402 


98412 


98122 


98433 


98443 


98453 


98464 


98474 


98184 


98194 


15 


3 


7 


9-98604 


98614 


98623 


98633 


98643 


98652 


98662 


98671 


98681 


98690 


14 


3 


6 


9-98792 


988U1 


98810 


98819 


988. >8 


98837 


98846 


98855 


9H864 


98872 


13 


3 


6 


9-98967 


98975 


98983 


98991 


99000 


99008 


99016 


99024 


99032 


99040 


12 


8 


5 


9-99127 


99135 


99142 


99150 


99157 


99165 


99172 


99180 


99187 


1)9195 


11 


2 


5 


9-99274 


99281 


99288 


99294 


99301 


99308 


99315 


99322 


99328 


99335 


10 


2 


5 


9-99407 


99413 


99419 


99425 


99432 


99438 


99444 


99450 


99456 


99462 


9 


2 


4 


9-99526 


99532 


99537 


99543 


99548 


99554 


99559 


995(15 


99570 


99575 


8 


2 


4 


9-99632 


99637 


99642 


99647 


99651 


99656 


99661 


91)660 


99670 


99675 


7 


2 


3 


9-99724 


99728 


99733 


99737 


99741 


99745 


99749 


99753 


99757 


99761 


6 


1 


3 


9-99803 


99807 


99810 


99814 


99817 


99821 


99824 


99828 


99831 


99834 


5 


1 


2 


9-99869 


99872 


99875 


99878 


99880 


99883 


99886 


99889 


99891 


99894 


4 


1 


2 


9-99921 


99923 


99926 


99928 


99930 


99932 


99934 


99936 


99938 


99940 


3 


1 


j 


9-99960 


99962 


99963 


99965 


99967 


99968 


99969 


99971 


99972 


99974 


2 





1 


9-99986 


99987 


99988 


99989 


99990 


99990 


99391 


99992 


99993 


99993 


1 





1 


9-99999 


99999 


99999 


99999 


00000 


00000 


00000 


00000 


00000 


00000 











27' 


24' 


21' 


18' 


16' 


12' 


9' 


6' 


3' 


0' 


o 


1' 


2' 


MEAN 


COSINES. DIFF. 



XV.-LOGARITHMIC 



HEAX 


DlFF. 





<y 


3' 


6' 


9' 


12' 


15' 


18' 


21' 


24' 


27' 


3CX 


I 


2' 





Inf. Neg. 


6-94085 


24188 


41797 


51297 


63082 


71900 


78595 


84394 


89511 


94086 






1 


8-24192 


20312 


28332 


30-263 


32112 


3:5880 


35590 


37229 


38809 


40334 


41807 






2 


8-54308 


55382 


56429 


57452 


58451 


50428 


60384 


61319 


62234 


63131 


64009 






3 


8-71940 


72659 


73366 


74003 


74748 


75423 


70087 


76742 


77387 


78022 


78049 






4 


8-84464 


85006 


85540 


80069 


86591 


87106 


87616 


88120 


88618 


89111 


89598 


171 


341 


5 


8-94105 


94630 


950(10 


95486 


95008 


96325 


96739 


97150 


97556 


97959 


98358 


138 


277 


6 


9-02162 


02525 


02H85 


03212 


03507 


03048 


04297 


04043 


04987 


05328 


05060 


117 


223 


7 


9-089 J 4 


09227 


01)537 


01)845 


101 :>o 


10454 


10756 


11050 


11353 


110-19 


11943 


101 


202 


8 


9-14780 


15054 


15327 


15508 


15867 


1(5135 


10401 


16665 


10028 


17100 


17450 


89 


178 


8 


9-19971 


20216 


20459 


20701 


20942 


21182 


21420 


21657 


21893 


22127 


22361 


80 


159 


10 


9-24(532 


24853 


25073 


25202 


25510 


25727 


25043 


26158 


26372 


26585 


20797 


72 


144 


11 


9-28805 


20067 


21)208 


20408 


296<)8 


29866 


30004 


30261 


30457 


30052 


30810 


66 


132 


12 


9-32747 


321)33 


a;} 11 9 


3U303 


Ml 87 


33670 


33853 


34034 


34215 


31300 


34576 


61 


122 


18 


9-36336 


86509 


3608 1 


36852 


37023 


37103 


37363 


37532 


37700 


37808 


38035 


57 


113 


14 


9-39077 


39838 


39999 


40159 


40319 


40478 


40636 


40795 


40952 


41109 


41266 


53 


106 


15 


9-42805 


42957 


43108 


43258 


43108 


43558 


43707 


43855 


44004 


44151 


44209 


50 


100 


16 


9-45750 


45892 


4(10.15 


40177 


46319 


4(5400 


40001 


46741 


4(5881 


47021 


47100 


47 


94 


17 


9-48534 


480(19 


48804 


4MK50 


40073 


40207 


49341 


40474 


49007 


40740 


40872 


45 


89 


18 


9-51178 


61306 


6i y 5 


51563 


51001 


51811) 


51946 


52073 


52200 


52320 


52452 


42 


85 


10 


9-53607 


53820 


53913 


54005 


54187 


54309 


54431 


54552 


54673 


54794 


54915 


41 


81 


20 


9-56107 


56224 


50312 


50150 


50570 


50603 


50810 


50926 


57042 


57158 


57274 


39 


78 


21 


9-58418 


58531 


586 14 


5H757 


58800 


5KOS1 


50004 


50205 


59317 


50429 


50540 


37 


75 


22 


9-60641 


00750 


00859 


00007 


01070 


61184 


01292 


01400 


61508 


01015 


61722 


36 


72 


23 


9-6-2785 


02890 


62996 


03101 


63205 


63310 


63414 


63519 


63023 


63726 


63830 


35 


70 


24 


9-64858 


61960 


65002 


65164 


65265 


65366 


65467 


65568 


65669 


65770 


65870 


34 


67 


25 


9-6C867 


66966 


67065 


67163 


67262 


67300 


67453 


67556 


67654 


67752 


67850 


33 


65 


26 


9-08818 


68914 


61)010 


01)106 


00202 


69208 


60303 


69488 


69584 


69679 


60774 


32 


64 


27 


9-70717 


70810 


70D04 


70907 


71000 


71184 


71277 


71370 


71462 


71555 


71648 


31 


62 


28 


9-72567 


72059 


72750 


72841 


72032 


73023 


73114 


73205 


73295 


73386 


73476 


30 


61 


29 


9-74375 


74465 


74554 


74G43 


74732 


74821 


74910 


74998 


75087 


75176 


75264 


30 


59 


30 


9-76144 


76231 


76319 


76406 


76493 


76580 


76668 


76754 


76841 


76028 


77015 


29 


58 


31 


9-77877 


77963 


78049 


78135 


78220 


78306 


78391 


78476 


78562 


78047 


78732 


28 


57 


32 


9-79579 


79663 


71)747 


79832 


70010 


80000 


80084 


801(58 


80251 


80335 


80419 


28 


56 


33 


9-81252 


81335 


81418 


81500 


81583 


81006 


81748 


81831 


81913 


81006 


82078 


28 


55 


34 


9-82899 


82980 


83002 


83144 


83225 


83307 


83388 


83470 


83551 


83632 


83713 


27 


54 


35 


9-84523 


84603 


84684 


84764 


84845 


81025 


85006 


85086 


85166 


85247 


85327 


27 


54 


36 


9-86126 


86206 


8G285 


80365 


80145 


8652* 


80603 


80683 


8(5762 


80842 


80921 


26 


53 


37 


9-87711 


87790 


878f>9 


87048 


8H027 


88105 


88184 


88262 


88341 


88420 


88408 


26 


52 


38 


9-89281 


89359 


81)437 


89515 


89503 


80071 


89749 


808-27 


89905 


89083 


90061 


26 


52 


39 


9-90837 


90914 


9091)2 


91009 


91147 


91224 


91301 


91379 


91456 


91533 


91610 


26 


52 


40 


9-92381 


92458 


92535 


92612 


92689 


92766 


92843 


92920 


92996 


93073 


93150 


26 


51 


41 


9-93916 


93993 


94069 


94146 


94222 


91299 


94375 


94452 


94528 


94604 


94681 


25 


51 


42 


9-95444 


95520 


95596 


95672 


95748 


95825 


95901 


95977 


96053 


96129 


96205 


25 


51 


43 


9-96966 


97042 


97118 


97193 


97269 


97345 


97421 


97497 


97573 


97649 


97725 


25 


51 


44 


9-98484 


98560 


98635 


98711 


98787 


98863 


98939 


99015 


99090 


99166 


99242 


25 


51 





60' 


57' 


54' 


51' 


48' 


45' 


42' 


39' 


36' 


33' 


80* 


r 


2' 


MEAN 


LOGARITHMIC DIFF. 



49 



TANGENTS. 



MEAN 


DIFK. 


33' 


S& 


89' 


42' 


45' 


48' 


51' 


54' 


57' 


60' 


o 


r 


2' 


7-98225 


02004 


05481 


08700 


11600 


14500 


17133 


10016 


21004 


21192 


89 






8-43232 


44611 


45948 


47245 


48505 


49729 


50920 


52070 


53208 


54308 


88 






8-64870 


65715 


66543 


67356 


08154 


68938 


00708 


70405 


71208 


71010 


87 






8-79266 


79875 


80476 


81008 


81653 


82230 


82799 


83301 


8301(5 


84404 


86 






8-90080 


90557 


91029 


91495 


91957 


92414 


92806 


93313 


93750 


91105 


85 


153 


306 


8-98753 


99145 


99534 


99919 


ooijol 


00079 


07()55 


01427 


01790 


02lT2 


84 


127 


253 


9-06002 


OG335 


OGGG6 


00904 


07320 


07043 


07001 


08283 


08(500 


081)14 


83 


108 


21ti 


9-12235 


12525 


12813 


13009 


13384 


13607 


13918 


14227 


14504 


14780 


82 


94 


189 


9-17708 


17965 


18221 


18475 


18728 


18979 


19229 


10178 


10725 


10071 


81 


81 


108 


9-22593 


22824 


23054 


23283 


23510 


23737 


2J962 


24180 


24410 


21032 


80 


76 


161 


9-27008 


27218 


27427 


27635 


27842 


28049 


28254 


28459 


28002 


288(55 


79 


69 


138 


9-31040 


31233 


31425 


31610 


31800 


31990 


32185 


32373 


32501 


32717 


78 


63 


127 


9-34755 


341)33 


35111 


35288 


35164 


35040 


35815 


35080 


30103 


30.530 


77 


59 


118 


9-38202 


38308 


38534 


38G09 


38803 


39027 


30100 


30353 


39515 


3'677 


76 


65 


109 


9-41422 


41578 


41733 


41887 


42041 


42195 


42348 


42501 


42053 


42805 


75 


61 


103 


9-44446 


44592 


44738 


44884 


45029 


45174 


45319 


45403 


45000 


45750 


74 


48 


97 


9*47299 


47438 


47576 


47714 


47852 


47989 


48120 


48202 


48308 


48f>34 


73 


46 


92 


9-50004 


50136 


502(57 


503'JS 


50529 


50659 


50789 


50919 


51048 


51178 


72 


43 


87 


9-52578 


52703 


52829 


52953 


53078 


53202 


53327 


53450 


53574 


53007 


71 


41 


83 


9-55035 


55155 


55275 


55395 


55514 


55633 


55752 


55870 


55989 


50107 


70 


40 


79 


9-57389 


57504 


57619 


57734 


57849 


57963 


58077 


58191 


58304 


58118 


69 


38 


70 


9-59651 


597(52 


59872 


59983 


60093 


60203 


60313 


60422 


60532 


00011 


68 


37 


73 


9-61830 


61036 


62043 


62150 


62256 


62362 


62468 


02574 


0'2080 


0-27H5 


67 


35 


71 


9-63934 


64037 


64140 


64243 


64346 


64449 


61552 


64654 


6 1750 


64X58 


66 


34 


69 


9-65971 


66071 


66171 


6G271 


66371 


66470 


60570 


66609 


60708 


00807 


65 


33 


66 


9-67947 


68044 


68142 


68239 


68336 


68132 


68529 


68626 


68722 


68818 


64 


32 


65 


9-09808 


69963 


70058 


70152 


70247 


70341 


70435 


70529 


70023 


70717 


63 


31 


03 


9-71740 


71833 


71925 


72017 


72109 


72201 


72293 


72381 


72476 


72507 


62 


81 


61 


9-73587 


73057 


73747 


73837 


73927 


74017 


74107 


74106 


74280 


74375 


61 


30 


60 


9-75353 


754 U 


75529 


75017 


75705 


75793 


76881 


75909 


70056 


76144 


60 


29 


69 


9-77101 


77188 


77274 


77361 


77447 


77533 


77619 


77700 


77791 


77877 


59 


29 


57 


9-78817 


78902 


78987 


79072 


V9156 


79241 


79320 


70110 


79405 


79579 


58 


28 


56 


9-80502 


80586 


800(59 


80753 


80S36 


80019 


81003 


81080 


81100 


81252 


57 


28 


55 


9-821(51 


82243 


82325 


82407 


8248i 


82571 


8'2053 


82735 


82817 


82809 


56 


27 


65 


9-83795 


83876 


83957 


84038 


84119 


84200 


84280 


84361 


84442 


84523 


55 


27 


64 


9-85407 


85187 


85567 


85647 


85727 


85807 


85887 


85967 


86046 


86126 


54 


27 


63 


9-87000 


87079 


87158 


87238 


87317 


87396 


87475 


87554 


87033 


87711 


53 


26 


53 


9-88577 


88655 


88733 


88812 


88890 


88968 


89046 


89125 


89203 


89281 


52 


20 


52 


9-90138 


90216 


90294 


90371 


90449 


90527 


90604 


90082 


90759 


00837 


51 


26 


52 


9-91688 


91765 


91842 


91919 


91996 


92073 


92150 


92227 


92304 


92381 


50 


26 


61 


9-93227 


93303 


93380 


93457 


93533 


93610 


93687 


93703 


93840 


93916 


49 


26 


51 


9-94757 


94834 


94910 


94986 


95062 


95139 


95215 


95291 


95308 


95444 


48 


25 


51 


9-96281 


96357 


96433 


96510 


96586 


96602 


96738 


90814 


90800 


96906 


47 


25 


51 


9-97801 


97877 


97953 


98029 


98104 


98180 


98256 


98332 


98408 


98481 


46 


26 


51 


9-99318 


99394 


99469 


99545 


99621 


99697 


99773 


99848 


99924 


00000 


45 


25 


61 


27' 


24' 


21' 


18' 


15' 


12' 


& 


6' 


3' ! O f 


c 


1' 


2' 


MEAN 


COTANGENTS. Dirr. 



LOGARITHMIC 



MEAN 


Dirr. 





a 


8' 


6' 


9' 


12' 


15' 


18' 


21' 


24' 


27' 


30' 


r 


2' 


45 


10-00000 


00076 


00152 


00227 


00303 


00379 


00455 


00531 


00606 


00682 


00758 


25 


51 


46 


10-01516 


01592 


01668 


01744 


01820 


01896 


01971 


02047 


02123 


02199 


02275 


25 


51 


47 


10-03034 


03110 


03186 


03262 


03338 


03414 


03490 


03567 


03643 


03719 


03795 


25 


61 


48 


10-04556 


04632 


04709 


04785 


0486 L 


04938 


05014 


06090 


05166 


05243 


05319 


25 


51 


49 


10-06084 


06160 


06237 


06313 


06390 


06467 


06543 


06620 


06697 


06773 


06850 


26 


51 


50 


10-07619 


07696 


07773 


07850 


07927 


08004 


08081 


08158 


08235 


08312 


08390 


26 


51 


51 


10-09163 


09241 


09318 


09396 


09473 


09551 


09629 


01)706 


09784 


09862 


09939 


26 


52 


52 


10-10719 


10797 


10875 


10954 


11032 


11110 


11188 


11267 


11345 


11423 


11502 


26 


52 


53 


10-12289 


12367 


12446 


12525 


12604 


12683 


12762 


12812 


12921 


13000 


13079 


26 


58 


54 


10-13874 


13954 


14033 


14113 


14193 


14273 


14353 


14433 


14513 


14593 


14673 


27 


58 


55 


10-15477 


15558 


15039 


15720 


15800 


15881 


15962 


16043 


16124 


16205 


16287 


27 


54 


56 


10-17101 


17183 


17205 


17347 


17429 


17511 


17593 


17675 


17757 


17839 


17922 


27 


55 


67 


10-18748 


18831 


18914 


18997 


19081 


19164 


19247 


19331 


19414 


19498 


19581 


28 


55 


58 


10-20421 


20505 


20590 


20074 


20759 


20844 


20928 


21013 


21098 


21183 


21268 


28 


66 


59 


10-22123 


22209 


22294 


22381 


22467 


22553 


22639 


22726 


22812 


22899 


22985 


29 


57 


60 


10-23856 


23944 


21031 


24119 


24207 


24295 


24383 


24471 


24559 


24647 


24736 


29 


59 


61 


10-26625 


25714 


2,0801 


25893 


25983 


26073 


20163 


26253 


26343 


26433 


26524 


80 


60 


62 


10-27433 


27524 


27616 


27707 


27799 


27891 


27983 


28075 


28167 


282CO 


28352 


31 


61 


63 


10-29283 


29377 


29471 


29565 


29659 


29753 


29848 


29942 


80037 


30132 


30226 


31 


63 


64 


10-31182 


31278 


81374 


31471 


81568 


81664 


31761 


31858 


31956 


32053 


82150 


32 


65 


65 


10-33133 


83232 


33331 


33430 


33530 


33629 


33729 


33829 


33929 


34029 


34130 


33 


66 


66 


10-35142 


85244 


85316 


35448 


35551 


35654 


35757 


86860 


35963 


36066 


36170 


84 


69 


67 


10-372 i 5 


37320 


37421] 


37632 


87(>38 


37744 


37850 


37957 


38064 


38170 


38278 


35 


71 


68 


10-89359 


89468 


89578 


39(587 


39797 


39907 


40017 


40128 


40238 


40349 


40460 


37 


73 


69 


10-41582 


41696 


41809 


41923 


42037 


42151 


42266 


42381 


42496 


42611 


42726 


38 


76 


70 


10-43893 


44011 


44130 


44248 


41367 


44486 


44605 


44725 


44815 


44965 


45085 


40 


79 


71 


10-46303 


46426 


46f. r >0 


4fi(J73 


46798 


46922 


47047 


47171 


47297 


47422 


47548 


41 


83 


72 


10-48822 


48952 


490K1 


41)211 


49341 


49471 


49602 


49733 


49864 


499% 


50128 


43 


87 


73 


10-51466 


51602 


61738 


51874 


52011 


52148 


62286 


52424 


62562 


52701 


52840 


46 


92 


74 


10-51250 


54394 


64537 


64681 


64826 


54971 


65116 


55262 


5540S 


65554 


65701 


48 


97 


76 


10-57195 


57347 


57499 


57652 


57805 


57959 


58113 


58267 


58422 


68578 


58734 


61 


103 


76 


10-60323 


60485 


60647 


60810 


C0973 


61137 


61301 


61466 


61632 


61798 


61965 


65 


109 


77 


10-63664 


63837 


64011 


64185 


64360 


64536 


64712 


64889 


65067 


65245 


65424 


69 


118 


78 


10-67253 


67439 


67627 


67815 


68004 


68194 


68384 


68575 


687C7 


68960 


69154 


63 


127 


79 


10-71135 


71338 


71541 


71746 


71951 


72158 


72365 


72573 


72782 


72992 


73203 


69 


188 


80 


10-75368 


75590 


75814 


76038 


76263 


76490 


76717 


76946 


77176 


77407 


77639 


76 


161 


81 


10-80029 


80275 


80522 


80771 


81021 


81272 


81525 


81779 


82035 


82292 


82550 


84 


168 


82 


10-85220 


85496 


85773 


86052 


86333 


86616 


86901 


87187 


87475 


87765 


88057 


94 


189 


83 


10-91086 


91400 


91717 


92036 


92357 


92C80 


98006 


93334 


93665 


93998 


94334 


108 


216 


84 


10-97838 


98204 


98578 


98945 


99321 


99699 


00081 


00466 


00855 


OT247 


0~1642 


127 


253 


86 


11-05806 


06244 


06687 


07134 


07586 


08043 


08605 


08971 


09443 


09920 


10402 


153 


806 


86 


11-15536 


16084 


16639 


17201 


17770 


18347 


18932 


19524 


20125 


20734 


21351 






87 


11-28060 


28792 


29535 


30292 


81062 


31846 


32644 


33457 


34285 


35130 


35991 






88 


11-45692 


46792 


47921 


49080 


50271 


61495 


62755 


54052 


65389 


56768 


58193 






89 


11-75808 


78036 


80384 


82867 


85500 


88304 


91300 


94519 


97996 


01776 


05914 






o 


60' 


57' 


54' 


61' 


48' 


45' 


42' 


39' 


36' 


33' 


30' 


r 


2 


MEAK 


LOGARITHMIC Dirr. 



MEAN 


DIFF. 


33' 


36' 


39' 


42' 


45' 


48' 


51' 


54' 


57' 


60' 


o 


i 1 


2 


10-00834 


00910 


00985 


01061 


01137 


01213 


01289 


013C5 


01440 


01516 


44 


25 


61 


10-02851 


02427 


02503 


02579 


02655 


02731 


02807 


028^(2 


02958 


03034 


43 


25 


51 


10-03871 


03947 


04023 


04099 


04175 


04252 


04328 


04404 


044*0 


04556 


42 


25 


61 


10-05396 


05472 


05548 


05625 


05701 


05778 


05H54 


05031 


06007 


06084 


41 


25 


51 


10-06927 


07004 


07080 


07157 


07234 


07311 


07388 


07405 


07542 


07619 


40 


26 


51 


10-08467 


08544 


08621 


08699 


08776 


08853 


08931 


09008 


09086 


09163 


39 


26 


62 


10-10017 


10095 


10173 


10251 


10329 


10407 


104X5 


10563 


10641 


10719 


38 


26 


52 


10-11580 


11659 


11738 


11816 


11895 


11973 


120.V2 


12131 


12210 


12289 


37 


26 


52 


10-13158 


1323S 


13317 


13397 


13476 


13555 


13635 


13715 


13794 


13874 


36 


26 


63 


10-14753 


14834 


14914 


14994 


15076 


15155 


16236 


15316 


15397 


15477 


35 


27 


64 


10-16368 


16449 


16530 


16612 


16693 


16775 


16856 


16938 


17020 


17101 


34 


27 


6t 


10-18004 


18087 


18169 


18252 


18331 


18417 


18500 


18f>82 


186(55 


18748 


33 


28 


55 


10-19665 


19749 


19X32 


19916 


20000 


20084 


20168 


20253 


20.KJ7 


20121 


32 


28 


56 


10-21353 


21438 


21524 


21609 


21694 


21780 


2 l.%a 


21051 


22037 


22123 


31 


28 


67 


10-23072 


23159 


23246 


23332 


23420 


23507 


23594 


23681 


23769 


23856 


30 


29 


68 


10-24824 


24913 


25002 


25090 


25179 


25268 


25357 


25146 


25535 


25625 


29 


30 


59 


10-20614 


26705 


26705 


26886 


2U977 


27068 


27159 


27250 


27311 


27 13U 


28 


30 


61 


10-28445 


28538 


28630 


28723 


28816 


38910 


29003 


29006 


29100 


29283 


27 


31 


62 


10-30321 


30416 


30512 


30607 


307U2 


30798 


30894 


30000 


31086 


81182 


26 


32 


64 


10-32248 


32346 


32444 


32542 


32640 


32738 


32837 


32935 


83034 


33133 


25 


33 


65 


10-34230 


34331 


31432 


31633 


346.34 


34735 


34836 


34938 


35010 


35112 


24 


34 


67 


10-36274 


36377 


36181 


36581! 


36600 


36795 


36899 


3700 4 


37110 


37215 


23 


35 


70 


10-38385 


38192 


38GOO 


38708 


38816 


38924 


39033 


39141 


30250 


;u>;j59 


22 


36 


72 


10-40571 


4068,5 


40795 


401)06 


41019 


41131 


41243 


41356 


4 1169 


4158-2 


21 


37 


76 


10-42842 


42958 


43074 


43190 


43307 


43424 


43541 


43658 


43776 


43893 


20 


39 


78 


10-45206 


45327 


45448 


45569 


45691 


45813 


45935 


46057 


46180 


46303 


19 


41 


81 


10-47674 


47800 


47927 


48054 


48181 


48309 


48437 


485i)5 


48604 


48S22 


18 


42 


86 


10-50260 


50393 


50526 


50659 


60793 


60927 


51061 


511*16 


51 Ml 


51166 


17 


45 


89 


10-52979 


53119 


53259 


63399 


63540 


53681 


53823 


63965 


51108 


54250 


16 


47 


94 


10-55849 


55996 


56146 


56293 


56442 


66592 


56742 


6681)2 


57043 


57105 


15 


50 


100 


10-58891 


69048 


59205 


59364 


59522 


59681 


50841 


60001 


60162 


60323 


14 


53 


106 


10-62132 


62:500 


62468 


62037 


62807 


62977 


63148 


63319 


63191 


63664 


13 


67 


113 


10-65604 


65785 


66966 


Gb 147 


66330 


66513 


66607 


66881 


67067 


67253 


12 


61 


122 


10-69348 


69543 


69739 


59936 


70134 


70332 


70532 


70732 


70933 


71135 


11 


66 


132 


10-73415 


73628 


73842 


74057 


74273 


74490 


74708 


74927 


75147 


75368 


10 


72 


144 


10-77873 


78107 


78343 


78580 


78818 


79058 


79209 


79541 


70784 


80020 


9 


80 


159 


10-82810 


83072 


83335 


83599 


83865 


84133 


84402 


81673 


81946 


85220 


8 


89 


178 


10-88351 


88647 


88944 


89244 


89546 


89850 


90155 


90163 


90773 


91 OHO 


7 


101 


202 


10-94672 


95013 


95357 


95703 


96052 


96403 


96758 


97115 


97475 


97838 


6 


117 


233 


11-02041 


02444 


02850 


03261 


03676 


04092 


04514 


04910 


45370 


05805 


5 


138 


277 


11-10889 


11382 


11880 


12334 


12894 


13409 


13931 


14460 


14994 


15536 


4 


171 


341 


11-21978 


22613 


23258 


23913 


24577 


25252 


25937 


26634 


27341 


28060 


3 






11-36869 


37766 


38681 


39616 


40572 


41549 


42548 


43571 


44618 


45692 


2 






11-59666 


61191 


62771 


64410 


66114 


67888 


69737 


71668 


73688 


75808 


1 






12-10490 


15606 


21405 


28100 


36018 


45709 


58203 


75812 


059T5 


Inf. 









27' 


24' 


21' 


18' 


15' 


12' 


9' 


6' 


3' 


: 


L 


1' 


2' 


MEAN 


COTANGENTS. Dirr. 



XVL-LOGARITHMIO 



MEAN 


DlFK. 





0' 


3' 


6' 


9' 


12' 


15' 


18' 


21' 


24' 


27' 


30' 


r 


2' 





10-00000 


00000 


00000 


00000 


00000 


00000 


00001 


00001 


00001 


0000 1 


00002 








1 


10-00007 


00007 


00008 


00009 


00010 


00010 


000 11 


00012 


00013 


00014 


00015 





1 


2 


10-00026 


00028 


00029 


00031 


00032 


00033 


00035 


00037 


00038 


00040 


00041 





1 


3 


10-00060 


00062 


00064 


00066 


00068 


00070 


00072 


00074 


00077 


00079 


00081 


1 


1 


4 


10-00106 


00109 


00111 


00114 


00117 


00120 


00122 


00125 


00128 


00131 


00134 


1 


2 


5 


10-00166 


00169 


00172 


00176 


00179 


00183 


00186 


00190 


00193 


00197 


00200 


1 


2 


6 


10-00239 


00243 


00217 


00251 


00255 


00259 


00263 


00267 


00272 


00276 


00280 


I 


3 


7 


10-00326 


00330 


00334 


00339 


00311 


00349 


00353 


00358 


00363 


00368 


00373 


2 


3 


8 


10-00425 


00430 


00135 


00411 


00446 


00452 


00157 


00463 


00168 


00174 


00180 


2 


4 


9 


10-00538 


00544 


00550 


00556 


00562 


00568 


00575 


00581 


00587 


00593 


00600 


2 


4 


10 


10-00665 


00672 


00678 


OOG85 


00692 


00699 


00706 


00712 


00719 


00726 


00733 


2 


5 


11 


10-00805 


00813 


00820 


00828 


00835 


00843 


00850 


00858 


00865 


00873 


00881 


2 


5 


12 


10-0091.0 


00968 


00976 


00981 


00992 


01000 


01009 


01017 


01025 


01033 


01042 


;{ 


5 


13 


10-01128 


01136 


01 lift 


01151 


01163 


01172 


01181 


01190 


01 199 


01208 


01217 


3 


6 


14 


10-01310 


01319 


01329 


01338 


01348 


01357 


01367 


01377 


01386 


01396 


0140G 


3 


6 


15 


10-01506 


01516 


01526 


01536 


01517 


01557 


01567 


01578 


01588 


01598 


01609 


3 


7 


16 


10-01716 


01727 


01738 


01749 


01760 


01771 


01782 


01793 


01*01 


01815 


01826 


4 


7 


17 


10-01940 


01952 


01961 


01975 


01987 


01999 


02011 


02022 


OJfW 


02046 


02058 


4 


8 


18 


10-02179 


02192 


02204 


02216 


02229 


02241 


02254 


02266 


02279 


02292 


02304 


4 


8 


19 


10-02133 


02146 


02159 


02472 


02185 


02199 


02512 


02525 


02539 


02552 


02565 


4 


9 


20 


10-02701 


02715 


02729 


02743 


02757 


02771 


02785 


02799 


02813 


02827 


0'28U 


6 


9 


21 


10-0298.) 


02999 


03014 


03029 


03043 


03058 


03073 


03088 


03102 


03117 


03132 


5 


10 


22 


10-03283 


03299 


03314 


03330 


03345 


03360 


03376 


03392 


03407 


03423 


03 138 


5 


10 


23 


10-03597 


03613 


03630 


03646 


03662 


03678 


031.95 


03711 


03727 


03744 


03760 


5 


11 


24 


10-03927 


03914 


03961 


03978 


03995 


04012 


04029 


04046 


04063 


04080 


04098 


6 


11 


25 


10-04272 


04290 


04308 


04326 


04343 


04361 


04379 


0^97 


04415 


04433 


04451 


6 


12 


26 


10-0 1634 


04652 


04671 


04690 


04708 


04727 


04746 


01764 


04783 


04802 


04821 


6 


12 


27 


10-05012 


05031 


05051 


05070 


050S9 


05109 


05129 


05148 


05168 


05187 


05207 


7 


13 


28 


10-05407 


05427 


05117 


05467 


05487 


05508 


05528 


05519 


05569 


05590 


05610 


7 


14 


29 


10-05818 


05839 


05860 


05881 


05902 


05924 


05945 


05966 


05988 


06009 


06030 


7 


14 


30 


10-06247 


06269 


06291 


06313 


06335 


06357 


06379 


06401 


06423 


06446 


06468 


7 


15 


31 


10-06693 


06716 


06739 


06762 


06785 


06808 


06831 


06854 


06877 


06900 


06923 


8 


15 


32 


10-07158 


07182 


07205 


07229 


07253 


07277 


07301 


07325 


07349 


07373 


07397 


8 


16 


33 


10-07641 


07665 


07690 


07715 


07740 


07765 


077K9 


07814 


07839 


07864 


07889 


8 


17 


34 


10-08143 


08168 


08194 


08219 


08245 


08271 


08297 


08323 


08349 


08375 


08401 


9 


17 


35 


10-08664 


08690 


08717 


08743 


08770 


08797 


08824 


08851 


08877 


08904 


08931 


9 


18 


36 


10-09204 


09232 


09259 


09287 


09315 


09343 


09370 


09398 


09426 


09454 


09482 


9 


19 


37 


10-09765 


09794 


09822 


09851 


09880 


09909 


09937 


09966 


09995 


10024 


10053 


10 


19 


38 


10-10347 


J0376 


10406 


10136 


10466 


10196 


10525 


10555 


10585 


10615 


10646 


10 


20 


39 


10-10950 ^1980 


11011 


11042 


11073 


11104 


11135 


11166 


11197 


11228 


11259 


10 


21 


40 


10-11575 


llbCC 


11638 


11670 


11702 


11734 


11766 


11799 


11831 


11863 


11895 


11 


21 


41 


10-12222 


12255 


12288 


12321 


12354 


12387 


12421 


12454 


12487 


12521 


12554 


11 


22 


42 


10-12893 


12927 


1'2961 


12995 


13030 


13064 


13098 


13133 


13168 


13202 


13237 


11 


23 


43 


10-13587 


13623 


13658 


13694 


13729 


13765 


13800 


13836 


13872 


13908 


13944 


12 


24 


44 


10-14307 


14343 


14 380 


14417 


14453 


14490 


14527 


14564 


14601 


14639 


14676 


12 


25 


o 


00' 


57' 


54' 


51' 


48' 


45' 


42' 


39' 


36' 


33' 


SO 1 


r 


2' 
























i 


MEAN 


LOGARITHMIC Din. 



53 



SECANTS. 



MEAN 


DlFF. 


33' 


38' 


39' 


42' 


45' 


48' 


51' 


54' 


57' 


60' 


o 


r 


2' 


10-00002 


00002 


00003 


00003 


00004 


00004 


00005 


00005 


00006 


00007 


89 








10-00016 


00017 


00018 


00019 


00020 


00021 


00023 


00024 


1)0025 


00026 


88 





i 


10-000-13 


00045 


00046 


00048 


00050 


00052 


0005 1 


00056 


00058 


00000 


87 


1 


i 


10-00083 


00086 


00088 


00091 


00093 


00096 


00098 


00101 


00103 


00100 


86 


1 


2 


10-00137 


00140 


00143 


00146 


00149 


00153 


0015G 


00159 


00102 


00106 


85 


1 


2 


10-00204 


00208 


00212 


00215 


00219 


00223 


00227 


00231 


00235 


00239 


84 


1 


3 


10-00284 


00289 


00293 


00298 


00302 


00307 


00,111 


00310 


00320 


00325 


83 


2 


3 


10-00378 


00383 


00388 


00393 


00399 


00404 


00109 


00414 


00419 


00425 


82 


2 


3 


10-00485 


00491 


00497 


00503 


00508 


00514 


00520 


00520 


00532 


00538 


81 


2 


4 


10-00006 


00612 


00619 


00625 


00632 


00638 


00645 


00052 


00058 


00605 


80 


2 


4 


10-00740 


00748 


00755 


00762 


00769 


00776 


00783 


00791 


00798 


00805 


79 


2 


5 


10-00888 


00896 


00904 


00912 


00920 


00928 


00930 


00944 


00952 


00900 


78 


3 


5 


10-01050 


01059 


01067 


01076 


01084 


01093 


01102 


OHIO 


01119 


01128 


77 


3 


6 


10-01226 


01235 


01244 


01254 


012b3 


01272 


01281 


01291 


01300 


01310 


76 


3 





10-01416 


0142C 


01435 


01445 


01455 


01465 


01475 


01485 


01495 


01500 


75 


3 


7 


10-01619 


01630 


01011 


01651 


01062 


01673 


01083 


01094 


01705 


01716 


74 


4 


7 


10-01838 


01849 


018GO 


01871 


01883 


01894 


01906 


01917 


01929 


01940 


73 


4 


8 


10-02070 


02082 


02094 


02106 


02118 


02130 


02143 


02155 


02167 


02179 


72 


4 


8 


10-02317 


02330 


02343 


02355 


02308 


02381 


02394 


02407 


02420 


02433 


71 


4 


9 


10-02579 


02592 


0260G 


02619 


02033 


02647 


02060 


02674 


02088 


02701 


70 


6 


9 


10-02855 


02870 


02884 


02898 


02913 


02027 


02941 


02956 


02970 


02985 


69 


6 


10 


10-03147 


03102 


03177 


03192 


03207 


03222 


03238 


03253 


03208 


03283 


68 


6 


10 


10-03454 


03470 


03486 


03502 


03517 


03533 


03549 


03505 


03581 


03597 


67 


5 


11 


10-03777 


03793 


03810 


03826 


03843 


03860 


03877 


03893 


03910 


03927 


66 


6 


11 


10-04115 


04132 


04150 


04167 


04185 


04202 


04220 


04237 


04255 


04272 


65 


6 


12 


10-04469 


04487 


04506 


04524 


0-1542 


04500 


04579 


04597 


04616 


01034 


64 


G 


12 


10-04840 


04859 


04878 


04897 


04916 


04935 


04954 


04973 


04993 


05012 


63 


6 


13 


10-05227 


05247 


05260 


05286 


05300 


05326 


05346 


05306 


06380 


05407 


62 


7 


13 


10-05631 


05651 


05672 


05693 


05714 


05734 


05755 


05776 


05797 


05818 


61 


7 


14 


10-06052 


06073 


06095 


06116 


OG138 


06160 


00181 


06203 


00225 


06247 


60 


7 


14 


10-06490 


06513 


06535 


00558 


OC580 


06003 


06625 


06648 


06671 


06693 


59 


8 


15 


10-06947 


06970 


06993 


07017 


07040 


07064 


07087 


07111 


07134 


07158 


58 


8 


16 


10-07421 


07445 


07470 


07494 


07518 


07543 


07507 


07592 


076 16 


07641 


57 


8 


16 


10-07914 


07940 


07965 


07990 


08015 


08041 


08000 


08092 


08117 


08143 


56 


8 


17 


10-08427 


08453 


08479 


08505 


08531 


08558 


08584 


08611 


08637 


08664 


55 


9 


17 


10-08958 


08986 


09013 


09040 


09067 


09094 


09122 


09149 


09177 


09204 


54 


9 


18 


10-09510 


09538 


09566 


09595 


09623 


09051 


09080 


09708 


09737 


09765 


53 


9 


19 


10-10082 


10112 


10141 


10170 


10199 


10229 


10258 


10288 


10317 


10347 


52 


10 


19 


10-10676 


10706 


10736 


10767 


10797 


10827 


10858 


10888 


109J9 


10950 


51 


10 


20 


10-11291 


11322 


11353 


11385 


11416 


11448 


11479 


11511 


11543 


11576 


60 


10 


21 


10-11928 


11960 


11993 


12025 


12058 


12091 


12123 


12156 


12189 


12222 


49 


11 


22 


10-12588 


12622 


12655 


12689 


12723 


12757 


12791 


12825 


12859 


12893 


48 


11 


23 


10-13272 


13306 


13341 


13376 


13411 


13446 


13482 


13517 


13552 


13587 


47 


12 


23 


10-13980 


14016 


14052 


14088 


14124 


14161 


14197 


14234 


14270 


14307 


46 


12 


24 


10-14713 


14750 


14788 


14825 


14863 


14900 


14938 


14976 


15014 


15051 


45 


13 


25 


27' 


24' 


21 


18' 


15' 


12' 


9' 


6' 


3 ( 


0' 





r 


2' 


MEAN 


COSECAJNTS. DIFF 



54 



LOGARITHMIC 



MKAN 


Dirr. 





(X 


3' 


6' 


9' 


12' 


15' 


18' 


21' 


24' 


27' 


3<X 


r 


2' 


45 


10-15051 


15089 


15127 


15165 


15204 


15242 


16280 


15318 


15357 


15395 


15434 


13 


25 


46 


10-15823 


15862 


15902 


15941 


15980 


16020 


1(5060 


16099 


16139 


16179 


16219 


13 


26 


47 


10-10622 


16662 


16703 


16744 


16785 


16826 


16867 


16908 


16949 


16990 


17032 


14 


27 


48 


10-17449 


17491 


17533 


17576 


17618 


17(5(50 


17703 


17745 


17788 


17831 


17874 


14 


28 


49 


10-18306 


18349 


18393 


18437 


18481 


18525 


18569 


18613 


18657 


18701 


18746 


15 


29 


50 


10-19193 


19238 


19284 


19329 


19375 


19420 


19466 


19511 


19557 


19603 


19649 


15 


30 


51 


10-20113 


20160 


20207 


20254 


20301 


20348 


20395 


20442 


20490 


20537 


20585 


16 


31 


52 


10-21066 


21114 


21163 


21212 


21201 


21309 


21358 


21408 


21457 


21506 


21555 


16 


33 


53 


10-22054 


22104 


22154 


22205 


22256 


221306 


22357 


22408 


22459 


22510 


22561 


17 


34 


54 


10-23078 


23130 


23183 


23235 


23288 


23310 


23393 


23146 


23199 


23552 


23605 


18 


35 


55 


10-24141 


24195 


24249 


24304 


24358 


24413 


24467 


24522 


24577 


24632 


24687 


18 


36 


56 


10-25244 


25300 


25356 


25413 


254(59 


25526 


26583 


25640 


25697 


25754 


25811 


19 


38 


57 


10-26389 


26448 


21)506 


2(5565 


2(5(523 


26682 


20741 


26800 


26860 


26919 


26978 


20 


39 


58 


10-27579 


27640 


27701 


277(52 


27823 


27884 


27945 


28006 


28068 


28130 


28191 


20 


40 


59 


10-28816 


28879 


28942 


29006 


29009 


29133 


29197 


29261 


29325 


29389 


29453 


21 


42 


60 


10-30103 


30169 


30235 


30301 


30H67 


30433 


30199 


30566 


30632 


30699 


30766 


22 


44 


61 


10-31443 


31511 


31580 


31619 


31717 


31787 


31856 


31925 


31994 


32064 


32134 


23 


46 


62 


10-32831) 


321)10 


32982 


3J051 


3,5125 


3311)7 


3J21.U 


33342 


33414 


33487 


33559 


24 


48 


63 


10-34295 


34370 


34144 


34519 


34591 


31669 


34746 


31820 


34896 


34971 


35047 


25 


60 


64 


10-35816 


35894 


35972 


36050 


36128 


36206 


36285 


36364 


36443 


36522 


36602 


26 


52 


65 


10-37405 


37487 


37568 


37650 


37732 


37814 


37896 


37979 


38061 


38144 


38227 


27 


55 


66 


10- 39069 


39154 


39239 


31)325 


39411 


31)497 


31)583 


39069 


31)756 


39843 


;59!);50 


28 


67 


67 


10-40812 


40902 


4091)1 


41081 


41171 


412(51 


41352 


41443 


41533 


41(525 


41716 


30 


60 


68 


10-42(542 


42736 


42831 


4-21)25 


43020 


43111 


4.5210 


43305 


4:5401 


43-11)6 


4351)2 


32 


63 


69 


10-44567 


44666 


44765 


44804 


441)64 


45064 


45164 


45265 


45365 


45466 


45567 


33 


67 


70 


10-46695 


46699 


40804 


46908 


47014 


47119 


47225 


47331 


47437 


47544 


47650 


35 


70 


71 


10-48736 


48846 


481)57 


41)067 


49179 


49200 


49402 


49514 


49626 


49739 


49852 


37 


74 


72 


10-51002 


51119 


51236 


51353 


61471 


51589 


51708 


51827 


51946 


52066 


52186 


39 


79 


73 


10-53406 


53531 


53655 


6:5780 


53005 


51031 


54157 


54284 


54411 


54538 


54666 


42 


84 


74 


10-55966 


56099 


56231 


56365 


56498 


56(533 


56767 


56902 


57038 


57174 


57310 


45 


90 


75 


10-58700 


58842 


58984 


59127 


69270 


59414 


59558 


59703 


59848 


69994 


60140 


48 


96 


76 


10-61632 


61785 


61938 


62091 


62245 


62100 


625f)5 


62711 


(52867 


63024 


63181 


62 


103 


77 


10-64791 


64956 


65121 


(5,V.'7 


65453 


6>620 


65788 


05957 


66126 


66296 


66466 


56 


112 


78 


10-68212 


68391 


68570 


M7!>0 


(58932 


61)113 


09296 


69479 


61)664 


69849 


70034 


61 


121 


79 


10-71940 


72136 


72332 


72029 


72727 


72927 


73127 


73328 


73530 


73733 


73937 


66 


133 


, 80 


10-76033 


76248 


76465 


76683 


76902 


77122 


77343 


77565 


77789 


78013 


78239 


73 


147 


81 


10-80567 


80807 


81048 


81291 


81535 


81780 


82027 


82276 


82526 


82777 


83030 


82 


164 


82 


10-85644 


85915 


86187 


8(3461 


8G737 


H7015 


87294 


87575 


87858 


88143 


88430 


93 


185 


83 


10-91411 


91720 


92032 


92347 


92663 


92982 


93304 


93628 


93954 


94283 


94614 


107 


213 


84 


10-98077 


98439 


98804 


99172 


99544 


99918 


00296 


00678 


01063 


01451 


01843 


125 


251 


85 


11-05970 


06406 


06846 


07290 


07739 


08193 


08651 


09115 


09583 


10057 


10536 


152 


303 


86 


11-15642 


16187 


16739 


17299 


17866 


18440 


19022 


19612 


20211 


20817 


21432 






87 


11-28120 


28849 


2959 1 


30316 


31114 


31896 


32692 


33503 


31330 


35173 


36032 






88 


11-45718 


46817 


47945 


49103 


50292 


51515 


52774 


54070 


55406 


66784 


58208 






89 


11-75814 


78042 


80390 


82872 


85505 


88307 


91304 


94522 


97998 


07777 


059T6 









60' 


6T 


54' 


51' 


48' 


45' 


42' 


39' 


36' 


33' 


30' 


1' 


2' 



LOGARITHMIC 



MEAN 
Dirr. 



SEC Aft T8 continued. 



55 



MEAN 


DlFF. 


83' 


36' 


39' 


42' 


45' 


48' 


51' 


64' 


57' 


60' 


o 


r 


2' 


10-15472 


15511 


16550 


15589 


15627 


15666 


15705 


15745 


15784 


15823 


44 


13 


26 


10-10259 


16299 


16339 


16379 


16419 


16460 


16500 


16541 


16581 


16622 


43 


13 


27 


10-17073 


17115 


17156 


17198 


17239 


17281 


17323 


17365 


17407 


17449 


42 


14 


28 


10-17916 


17959 


18002 


18045 


18089 


18132 


18175 


18219 


18262 


18306 


41 


14 


29 


10' 18790 


18834 


18879 


18924 


18968 


19013 


19058 


19103 


19148 


19193 


40 


16 


30 


10-19695 


19741 


19787 


19834 


19880 


19926 


19973 


20019 


20066 


20113 


39 


16 


31 


10-20633 


20G81 


20728 


20776 


20824 


20872 


20921 


20969 


21017 


21066 


38 


16 


82 


10-21605 


21654 


21704 


21754 


21803 


21853 


21903 


21953 


22003 


22054 


37 


17 


33 


10-22613 


22664 


22715 


22767 


22819 


22870 


22922 


22974 


23026 


23078 


36 


17 


34 


10-23658 


23711 


23764 


23818 


23871 


23925 


23979 


24033 


24087 


24141 


35 


18 


36 


10-24742 


24798 


24853 


24909 


24964 


25020 


25076 


25132 


25188 


25244 


34 


19 


88 


10-25868 


25926 


25983 


26041 


26099 


26157 


26215 


26273 


26331 


21)389 


33 


19 


39 


10-27038 


27098 


27157 


27217 


27277 


27337 


27398 


27458 


27518 


27579 


32 


20 


40 


10-28253 


28315 


28378 


28440 


28502 


28565 


28627 


28690 


28753 


28816 


81 


21 


42 


10-29518 


29582 


29647 


29712 


29776 


29841 


29907 


29972 


30037 


30103 


30 


22 


43 


10-30833 


30900 


30968 


31035 


31103 


31171 


31238 


31306 


31375 


31443 


29 


23 


45 


10-32204 


32274 


32344 


32414 


32485 


32555 


32626 


32697 


32768 


32839 


28 


24 


47 


10-33632 


33705 


33779 


33852 


33925 


33999 


31073 


34147 


34221 


34295 


27 


25 


49 


10-35123 


35200 


35276 


35353 


35429 


35506 


35583 


35661 


35738 


35816 


26 


26 


51 


10-36681 


36761 


36841 


36921 


37001 


37082 


37162 


37243 


37324 


37405 


25 


27 


64 


10-38311 


38394 


38478 


38562 


38616 


38730 


38814 


38899 


38084 


39069 


24 


28 


56 


10-40017 


40105 


40192 


40280 


40368 


40457 


40545 


40(534 


407-23 


40812 


23 


29 


69 


10-41808 


41899 


41992 


42084 


42176 


42269 


42362 


42455 


42549 


42642 


22 


31 


62 


10-43689 


43785 


43882 


43979 


44077 


44174 


44272 


44370 


44468 


44667 


21 


3 '2 


65 


10-45069 


45771 


45873 


45976 


46078 


46181 


46284 


46387 


46491 


46595 


20 


31 


68 


10-47758 


47865 


47973 


48081 


48189 


48298 


48407 


48516 


48026 


4873H 


19 


36 


72 


10-49966 


50080 


50194 


50308 


50423 


50538 


50653 


60769 


50885 


5100'2 


18 


38 


77 


10-52306 


52427 


52548 


52670 


52791 


52914 


53036 


53159 


53283 


53406 


17 


41 


81 


10-54794 


54923 


55052 


55181 


55311 


55441 


55572 


55703 


55834 


651)66 


16 


43 


87 


10-57447 


57584 


57722 


67860 


57999 


58139 


58278 


58418 


58559 


58700 


15 


46 


93 


10-60287 


60434 


60582 


60730 


60879 


61029 


61179 


61330 


61481 


61632 


14 


50 


99 


10-63340 


63498 


63G58 


63818 


63978 


64140 


64302 


64464 


61627 


64791 


13 


54 


107 


10-66638 


6G810 


66982 


67156 


67330 


67505 


67681 


67857 


68034 


68212 


12 


68 


116 


10-70221 


70409 


70597 


70786 


70976 


71167 


71359 


71552 


71746 


71940 


11 


63 


127 


10-74142 


74348 


74555 


74763 


74972 


75182 


76393 


75605 


75819 


76033 


10 


70 


140 


10-78466 


78694 


78924 


79155 


79387 


79620 


79855 


80091 


80328 


80567 


9 


78 


155 


10-83284 


83540 


83797 


84056 


84317 


84579 


84843 


85109 


85376 


85644 


8 


87 


174 


10-88719 


89010 


89303 


89598 


89894 


90193 


90494 


90798 


91103 


91411 


7 


99 


198 


10-94948 


95285 


95624 


95966 


96310 


96658 


97008 


97361 


97717 


98077 


6 


115 


230 


U'02238 


02637 


03040 


03447 


03857 


04272 


04690 


05113 


05539 


05970 


5 


137 


275 


11-11020 


11510 


12005 


12506 


13013 


13526 


14045 


14571 


15103 


15642 


4 


170 


339 


11-22057 


22690 


23333 


23985 


24647 


25320 


26003 


26697 


27403 


28120 


3 






11-36909 


37804 


38718 


39651 


40605 


41581 


42579 


43600 


44646 


45718 


2 






11-69680 


61204 


62783 


64422 


66125 


67897 


69745 


71676 


73696 


76814 


1 






12-10491 


15607 


21406 


28100 


36018 


45709 


58203 


75812 


05915 


Inf. 









27' 


24' 


21' 


18' 


15' 


12' 


9' 


6' 


3' 


0' 





1' 


2' 


MEAN 


COSECANTS. DIFF. 



w 

a 



>v^ -j 

^O H^ 



HH 

T 



M 



^2 t , .5 CN 










22S 




































00 


bbbbb 










bbbbb 












1 


632 










cs oo t>- to o 

CM O 00 T-* ^ 












o 


























rHCO0 










,H<NCO<*Q 














lu io co o oc >o ci o t- '"o cS 
^5* .-t co 10 co co o ci cc 'O r- 
)O OOOOO i i ' i i i i ^ 


"rf Ci O O >O 
>^ CN CN CM C4 


-" CO i-t t^ CN 

! Cl ~i CN *}* 


t- CO 00 CO CS 
1 CJ CO -^ O 

S CO CS CO 

cp co co rf" rh 


o -n- Oi -r TO 

OJ Cl CO T 
>O CO 00 O 1-* 


T-H CO -< t>- CM 
CO 1^ CN CO i-H 


CO J< T-I 00 CO 
CM TI CO t^. Ci 

tpcpcp cpcp 


CO CN t^ CM CO 

CO i-H OO CO CO 
i i CO T CO 00 


-H co co co o 

O TH CO >O t- 


iO CO O 00 
O CM "f to 
OS Cl OS Cl 


t- Cl T-I (M "*< 

OS Cl O O O 


s 


CO CM t>- <N 00 COOO-^OS^ 

Cl TP GO CO r CM CO I tO O 
QQ CO 1-1 00 CO CO TH OO CO CO I 


O O O CO 1-1 

CO >0 CO O 00 
00 O (M rji O 


co <N r>. CM oo 

1- C-l CO 1 O 


o * ci co oo 

CO OO OS <-H CO 


CS >O O O T- 

O CO CO O <M 


iO O ** Cl CO 

t^ o CM 01 r~ 

CO >O C-- OO O 




T-I CN "J CO OO 


tO i ( t>- CN t- 

CO 00 CM t>- i 1 

Cl CO r*< 1-1 Cl 
Ci i t CO >O CO 


CO O CN CO to 


os >o o o TH 

CO CO 00 <N t^- 
CO T-I CO CO CO 

t os o CN n 1 


s? 





.... 


***** 




***** 














T^TH^ 




ci r~ ci oo co 00^05^0 

Ci CO-HiOO -v Cl CO 00 CO 
/vi Cl C. I -. -T Cl C; CO -r Ci 
JfJ i-< Cl -p CO CO Ci CO O CO 

TJI ooooo 7 7 "~ < 7 1 


11111 


r- cs o <M f 

CN (M CO CO CO 


CN r- -< co i i 

i CO CO CO i-l 
CO t^ CS -H CO 

cp cp cp -<t< TI< 


f CO CO O -< 
T* 1 xt< rp p >p 


CM l~ <N 00 CO 
CC' CM t- 1 CO 

co io ft So o 

O O iO iO CO 


O >O Ci rP OS 
Cl rp lo r>- OS 

cp cp tp cp cp 


OCO rH tO 
00 CM t^ TH 
(^ tO CN O 

TH CN -f CO 00 


<M t>- CN CO CO 

to O to Cl -4i 

t>. 10 CN ci r>. 

Cl TH CO ^ CO 


oo *< cs HH o 

CO CO I CN t>. 


CM CS (>. ti TH 
t- OO O CM -t" 
Cl Cl 


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!>. CO CO CO OS -*< CS O O >O 
-P C. CO OC Cl I- 1 CO *H >0 
JYK O 1- >O d O t O CM O t- 
g .1, <M -* CO 00 CS TH CO '0 CO 
VJ OOOOO O i i i 11 


>O CN Ci t^- -^ 
00 O * CO O 
i-H CN CN CN CN 


r>. CN oo co oo 

S CN CO CO CO 


<st OS ^ O O 
O Cl -<Ji OS CO 
CS CO -f T-H CS 
>O t- CS T- < CN 
CO CO CO T ^ 


CN rt . to 
-^ T-I CS CO 

<f CO OO Ci 1 


O iO Cj rr OO 
T i i QO CO CO 
CO O CO 00 O 


C-l CO O I' OS 
CO CO CO CO CO 


O to TH tO tM 

to o o os -j< 

00 CO CO O 00 
O CN rf CO !-- 


t> CM 00 CO 00 
OO CO 1 ^ CM CO 
O CO O OO 'O 

OS -i CO^PCO 

t-- cp op op op 


11111 


O CO TH CO CM 
-^ CO CO t>. CM 

o t^ o ci o 
r- oo o ci rp 

Cl Cl O O O 


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XVIII. CONVERSION OF TIME AND ANGULAR 
MEASURE. 



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1 


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120 


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rH?2cOOO *?^^^^ 



COOCOl^-OS rHCO-^tl>O"O lO-^CO'^l'H OSCD-frHOO OrHt-~.COCO ^OSCOOOCO 
OCOOl^-OS (N^COOOO CMrfiCDOOO rHCOuOr^OO OCNCO'OCO OOOSrH^-r^ 



^(TJrHfDOS rHtOU5OS<N rfrv.COCOOO OOSt>.OO tOOOOOOO rHCNOtOCN 

CD OS CO I CO UJrHCOO-^ COOOOOOCM >rrHCDOOl>. COt>t>.CDrH lOCOOrHCD 

COl^rH^t, OJrHtNCOCO COCSC-40CT " ~ " "- -" 

O<MOI-O> rH -* CO 00 O *" ~" ' n ~~ " 



. 

J1 rH CO 
t- >O ^< 



CS^CDOOOS rHCO'OCOOO OrHCOOCO 00 O> rH W* 

to to cp cp cp ^ l ^ ^ i.- l .- ojo op ojo oo w op op os os at 



CO 



o CN **< i^- at 





5^rH t--^tlCOCDO O Ol -^ iO h- rHQOOOCOCO OseNOJrHQO 

300O CJ-^CDl-OS rHCOlOCOOO OrHCOOCO OOOSr^CM-r^ 
jiOCD COCDCpCDtO t>-t>t>.t>-t-* 0000000000 OOOOOSOSO* 



10 5 



rH 00 rH OS CO 

_ -.COOCN iccDooooos 

COTjiTf^Tj* lOiO^OiOiO 



os o eo o o O to o & os 

COOCM'HCD OOCOO^T^CO 

O5OSQOI~-O COrHOSCOCO 

rHCOlOt^OS rHCO-fCOOO 



o ^f >o -^ o *<** CD o c) t> 

OCO<NOO-*I os^rc-^^oo 

OrHCO-^CD l- OS O Ol CO 

OO 00 00 00 00 OO 00 OS Os OS 



-f O <O t- 
Ci <N 



COrHTfrHt> HkO<NeOOO OlOOtOCOrH OOIOOOOCO ^rHCOOSp 

OSI-OO5CO rfOCOCMt>. OSQO^t^l^ ^OOO500O OSrHOl^CO 

. <N^COCDI>. t>l^COiOCO rHOSl^^rH OOrfOCDOl l-COOO(Nt>. 

COOS r-COOI-OS rHCOOt>.OS rHIM'fCOOO OSrHCQ-<TCO tjOSOCMCO 

Tf^ti kTJiOiO'O'O tOCOCOCOCO t* l> ! l" I"* l>00000000 OOQOOSOSOS 



t ooo t- o 

CO 00 CM >O OO O 



<NtOCO>O-^< CNrHrHlCTt< OJrHOJOlCM OOSOOOI>. rHOOOO4Cl 

t>.OOSOOCO rfrH^COOS rHrHb-OO t-rHCOCOOS ^ItO'OCOQl 

_ OCMCO^iO kOiO^COrH OOOOCOO tOCOOSiOO tOrHtOrHif 

00 rHCOOt>-OS rHCOkCt^OS rHCN^lCDOO CJSrH(MTrCO t^OSOOJO 

^ lO'O'O'OiO tOCOtOCOCO t-l>t->l^I> t>.00000000 OOOOOSOSC 



00O 1 **tO'^ rHOSrHt>.rH COUSOt^O OOCOt'.O 1 ^ OSCOt^OlO* t>OOSCOM 

(NOOOOCMrH OCOOOl^CO tJirHO^rH COCOOSCOCO OOl>.t-Tj< OOfHOOO-rf 

rH iO OS CO CO OOOrlOlCO COCOCMrHO OOCOCOrHOO lO-Ht^-COOS -^lOlOOS^ 

- '- -7S rHCO>Ot-OS OO1^COI> OSrHCMTtiiO t^O>Or-.cO 

O tOCOCOCOCO t- !> t> I- O- t^- 00 OO 00 00 OO OO OS Ci OS 



fS rH CO CO 00 O CI 

3 "f "*! ^ ^ C 



o co Oi o r>- 

CO <M CD I- CM 

to oo a> o ^ 

O <N Tf t^ OS 



OOl^Ot- OSO(NrfiO l^OOOr-.eO 
t^*tI>l>t I" OJO 00 00 00 OO 00 OS OS C5 



OSOSOOCNO OOCDCOO1"* 
040SOCOCO OO^COCN 






..^ -. t* t- O A tOOsifttfSC 

t>.^ t^.l-'^OOOJ tOliOOCi 

t^CO ^JO)Ot>.'' rHOO^rOC; 

5?2 P w .>r o j* pocNsju 



. 

00 O rH OS >O 
t OOO r-l CO 

00 00 OS OS OS 



tpCDt-QOCD prHWCO^ iOCDt^OOOD 

tbibibibud CD cb co CD co Qocococoob 



CM CM CM CM CM 


O 00 O ^ CO 


CM rH OS 00 tO 

rH rH 


sss 


SOS t^. to iO 
Ji OiO> 


kO rf CO CM rH 
OiOl Oi Oi OS 


CO 


, 














32SSS 


tO kO CO CM rH 

o o o o 


Oi 00 b- to-* 
Ci Ci Ci Cl O> 


^ CO rH 

CiOiCiOl 


Oi CO tO to kO 


ff CO CJ Cl rH 

00 00 00 00 00 


00 
















escort* 


COCMOOSCO 


r* to ko ^ co 




oo r- to o -^ 


^ CO CM rH rH 




CiOiCiOiOi 














O Tf CO CM 
OO 00 00 00 00 


cs i> to to 

00 l>- l> I* I- 


Tt< rr CO CM r-t 
t>. t- 1- l>. t- 


00 00 t-. 

L" t- tO tD tO 


JBSi2SS 


CO Cl Cl i -H 

to to to to to 


CD S 


t- t> to to <o 


to to to to to 


CM Cl rH OS 


Oi 00 t^. t^ to 


to >o rr rr co 


CO Cl 71 rH -H 


. 
IO 

. 


t^tOkO^ 


CO CM CM r-IO 


OS 00 00 t" 


t-. tO to kO kO 


rji rr CO CO CM 


CJ 71 -H rH 






kO kO kO kO kO 










5 


CO CM rH -HO 


988S8 


r>- 1 to to >o 


>O >O rT rr rft 
CO CO CO CO CO 


CO CO rM Cl CM 

co co :o co co 


<M rH ^H -H 


CO 


oo oo co r>. t>. 

CM CJ CM CM CM 


t>- to to kO kO 
CM CM CJ CM CM 


CM CM CJ CM C 


CO CO CO CO 71 

CM CJ c CJ CJ 


Cl 71 71 i 1 


_| rH rH O 

CJ CJ CJ Cl CM 


<N 


T*< rt< rT rt< CO 


C7. CO CO CO CO 


Cl Cl Cl Cl Cl 


Cl Cl rH rH -H 


_ ^H , ^_ ^ 


rH - C 


rH 
















Oi Ci CO 1- 


CO CM rr O Ci 

GO Ci 00 O rH 

tO Ci CJ kO OO 

CM co kO to r> 
o o o o o 


CO rH >O rfl Ci 

to os o oo 
ci ko i - oo 

rH rH rH rH 


U - r-l -0 rH 

(^ 1 CO Ci rH 

C CM CO rr tO 
kO tO (>. 00 Ci 


r^ ^-! Ci O 7"l 

I- CO CC C- 

o rH 7J :o vO 

d CM CJ CJ CM 


ci cs cr ci oo 

l~ *O >~ >O 

to i oo Ci o 

CJ CJ CJ 7J CO 


CO 


CM 














> O CO t - CO 
Cl CO t 1 - 71 

1- rH kO 00 CI 

kO I- CO C- I 
Ci Ci Oi Cj O 


rH CM tO CO r}1 
kO tO kO CO Ci 
kO 00 rH rp tD 
CJ CO iO tO l^ 

o o o o o 


CO tD CO OO 1 ^ 

Ci rH CC >O l^ 
C/J O rH 71 CO 


5^S 

Ci i CJ CO 'O 
rj< tD l-^ GO Ci 


to i- i- 00 Ci 

O i CJ CO * 


OC tO rf rH OO 

to O :- "O >O 
OS 

CM ci 71 7J "O 


00 
















tO -H to CM OS 

kO C* CO t - O 
kO tO CO Ci rH 
C, CiC.Cs 


rH CO CJ O tO 
rr I- CO kO 

CM CO kO tO I 

00000 


o t^- co kO co 

rH rj< tO tO IO 
00 CJ rr tO 


t-. h- ^ t>- Cl 

Cl CO CO tO CO 

CO Ci rH CJ CO 
rr to t- 00 Ci 


fe^l^jO^ 

O rn T 1 CO rr 
7 1 71 CJ CJ CJ 


CO CO 71 O CO 
to '0 iC iO 
00 Ci CV C. Ci 
kO tO I - CO Ci 
CJ CJ "1 7J 7J 


l> 
















kO 1 00 tO tO 

rr CO 


00 O Oi l~ rp 


Ci Cl 4f rf CO 


2SSI: 


5 f? r? 


Ci ci Ci Ci oo 

kO Ci 71 -*i O 




Oi Ci Ci Ci O 


CJ CO rr tO t- 
O O O O 


gg^^JS 


rr 10 i>- co ci 


O rH 71 CO f 
CM CJ CJ 7J CM 


kO O 1 - CO Cl 
CJ 7J CJ CJ CJ 


















CO rH rH 

kO to CO OS O 
Oi Ci Ci Ci O 


JO rHCS rH b- 

CM CO rr CO t>. 
O O O O O 


t>. (N rH tO t 

tO O CJ CJ rH 

kO OO CD Cl rfl 
OO Ci T-H CJ CO 
rH rH rH 


CO tO >O Cl >O 

Ci >o ^r to 

kO I - Ci O rH 

rr iO to CO Ci 


to 'O ci ao <i 

t - 1 ^ tO CO O 

CJ CO rr O tO 

CJ 71 CJ CM CM 


f to r~ t~ i- 

kC Ci Cl rr >O 

to to t - i - i - 

c to i- co c* 

Cl 71 71 71 71 


o 
















rH rH CM rt< t^ 

to t- to co oo 

ii o ci co to 

kO to I- Oi O 


CM O O rf rH 
CJ T rr CM CJ 
O CO tO Ci rH 
CI CO rr. kO 


CO Oi tO CO 

rr i O O Ci 
rf tO Ci rH CJ 

CO Ci O Cl CO 


tO O rH Ci rh 

<? to i^ cs o 


to to jo co c* 


Ci CJ -HH tD t^ 

kc o io r o to 
ko to i^- co cs 



















rH CO CJ OS kO 
O rr 00 rn IO 

kO to i> os o 


O Cl rH tO kO 

00 CJ kO l- O 

rn CO rr kO ! 



CO to Oi tO 
rH IO 1- CO 00 
CO >O l-^ Ci rH 

OO Ci O rH CO 
O -< rH rH 


01 rf< t> tO CM 

co to oo cs 


kO t^ tO rf< 

iO O rr 7J OS 


t CO -H rT tO 

*f co CJ fi ko 

rr rr iO >O >O 
>O 'O I~ CO Ci 


CO 
















CO rH kO rH 00 
1- Ci OO tO rH 
CC 71 tO O rr 
rf O l^ Ci O 
OI Ci Ci Ci O 


kO t- 00 tO CO 
I- CO to OS 
-H CO rfi kO to 

o o o o 


^ CO t- tO -H 

Ci CO iO O tO 
rH rr CO CO O 
CO gO rH CO 


CM Ci CM CJ 
f O to O ^O 
CM rr iO 1 - CO 
rr O ^ l>- CO 


rf t>. GO tO r)H 
rr rr co rH CO 
OS O i CJ CJ. 
C- i CJ CO rM 
rH CJ CJ CJ CM 


01 rr os ci >G 

CO 00 rH T O 
CO CO rp T TT 


. 


rf< O t- rf< CO 

CO kO xfi CM 00 

|~ r^ ift Ci CM 

rr tO t^ 00 O 


rf< tO CM O CO 

CM rr iO rr rH 


Cl kO tO CM 

CO C. O -- CM 

rH -H rH 


CJ r^ CC rH 

r?oS|^00 


CO CO CJ O t^ 

00 Cl -4 
Ci O Cl -O rn 
rH CJ CJ 7J Cl 


rp tO rfi 

kO tO l>- CO Ci 
CM CM CM CJ CM 


iH 
















OS O O 00 * 
i 8 E 00 


O kO CM CM tO 

Oi rH CM rH CO 
T 00 rH Tf< tO 

O 


<*< to co to co 
rr oo rH cj o 

OS i-H TJI tO OO 

!>. OS rH CJ) 


t- tO CM kO kO 


CM !>. rH rH 
Cl CJ CM t>. 

t>- 00 Ci 


OS O CO 00 CO 

CM rH CO O 

rH rH CM CM CM 


o 




CM CM CM <N CM 


CM CM CM CM CM 


CM CM SM CM CM 


CM CM CM CM CM 


CM CM CM CM CM 




&ss 


IQ9>>99 


00 GO 00 00 00 


pCDt-OOO> 


CO CO CO CO CO 


CO CO CO CO CO 





6 4 



XXI. EXPONENTIAL AND HYPERBOLIC FUNCTIONS. 



X 


* 


-* 


COHII X 


SINII x 


X 


e* 


~ 


COSH x 


SINK x 


00 


1-00000 


I'OOOOO 


1-00000 


00000 


50 


1*64872 


GOG53 


1-12763 


52110 


01 


01005 


99005 


1-00005 


01000 


51 


1-66529 


60050 


1-13289 


53240 


02 


02021 


98020 


1-00020 


02000 


52 


1-68203 


50452 


1-13827 


54375 


03 


03046 


97045 


1-00045 


03000 


53 


1-69893 


58860 


1-14377 


55516 


04 


04081 


96080 


1-00080 


04001 


54 


1-71601 


58275 


1-14038 


56663 


05 


05127 


95123 


1-00125 


05002 


55 


1-73325 


57695 


1-15510 


57815 


06 


0(5184 


94177 


1-00180 


00004 


56 


1-75067 


57121 


1-16094 


58073 


07 


07251 


93239 


1-00245 


07006 


57 


1-76827 


56553 


1-16690 


60137 


08 


08329 


92312 


1-00320 


08009 


58 


1-78604 


55990 


1-17207 


01307 


09 


09417 


91393 


1-00405 


09012 


59 


1-80399 


55433 


1-17016 


62483 


10 


10517 


90481 


1-00500 


10017 


60 


1-82212 


54881 


1-18547 


G3GG5 


11 


11628 


89583 


1-00606 


11022 


61 


1-84043 


54335 


1-10180 


04854 


12 


12750 


88692 


1-00721 


12020 


62 


1-85893 


53704 


1-10844 


66049 


13 


13883 


87810 


1-00846 


1 3037 


63 


1-87761 


53259 


1-20510 


07251 


14 


15027 


86936 


1-00982 


14046 


64 


1-89648 


52720 


1-21189 


08459 


15 


16183 


86071 


1-01127 


15056 


65 


1-91554 


52205 


1-21879 


69675 


16 


17351 


85214 


1-01283 


10008 


66 


1-93479 


51G85 


1-22582 


70897 


17 


18530 


84 366 


1-01448 


170S2 


67 


1-95424 


51171 


1-23207 


72120 


18 


19722 


83527 


1-01 (.24 


18007 


'68 


1-97388 


50662 


1-24025 


73363 


19 


20925 


82696 


1-01810 


19115 


69 


1-99372 


50158 


1-24765 


74G07 


20 


22140 


81873 


1-02007 


20134 


70 


2-01375 


49G59 


1-25517 


75858 


21 


2.1368 


81058 


1-02213 


21155 


71 


2-03399 


40164 


1-26282 


77117 


22 


2-1608 


80252 


1-02430 


22178 


72 


2-05443 


48075 


1-27050 


78384 


23 


258(50 


79453 


1-02657 


23203 


73 


2-07."08 


48101 


1-27850 


79659 


24 


27125 


78663 


1-02394 


24231 


74 


2-09594 


47711 


1-28652 


80941 


25 


28403 


77880 


1-03141 


25261 


75 


2-11700 


47237 


1-20468 


82232 


26 


2%93 


77105 


1-03390 


2G294 


76 


2-13828 


46767 


1-30207 


83530 


27 


30990 


76338 


1-03607 


27320 


77 


2-15077 


46301 


1-31139 


84838 


28 


32313 


75578 


1-03040 


28367 


78 


2-18147 


45841 


1-31994 


86153 


29 


33643 


74826 


1-0 1235 


29408 


79 


2-20340 


45384 


1-32862 


87478 


30 


34986 


74082 


1-04534 


30452 


80 


2-22554 


44033 


1-33743 


88811 


31 


36343 


73345 


1-04844 


3141)0 


81 


2-24791 


4448(5 


1-34638 


90152 


32 


37713 


72615 


1-05164 


32540 


82 


2-27050 


44043 


1-35547 


91503 


33 


39097 


71892 


1-05495 


33602 


83 


2-20332 


43605 


1-36468 


02863 


34 


40495 


71177 


1-05836 


34650 


84 


2-31637 


43171 


1-37404 


94233 


35 


41907 


701GO 


1-00188 


35710 


85 


2-33965 


42741 


1-38353 


95612 


36 


43333 


697G8 


1*00550 


36783 


86 


2-36316 


42316 


1-39316 


97000 


37 


44773 


G9073 


1-06923 


37850 


87 


2-38091 


41805 


1-40293 


98398 


38 


40228 


6838G 


1-07307 


38921 


88 


2-41000 


41478 


1-41284 


99806 


39 


47698 


67706 


1-07702 


39996 


89 


2-43513 


41066 


1-42280 


1-01224 


40 


49182 


67032 


1-08107 


41075 


90 


2-45000 


40657 


1-43309 


1-02652 


41 


50682 


66365 


1-08523 


42158 


91 


2-48432 


40252 


1-44342 


1-04090 


42 


52196 


65705 


1-08950 


43246 


92 


2-50920 


30852 


1-45390 


1-05539 


43 


53726 


65051 


1-0938H 


44337 


93 


2-53451 


39455 


1-46453 


1-06003 


44 


55271 


64404 


1-09837 


45434 


94 


2-55998 


39063 


1-47530 


1-08468 


45 


5G831 


637G3 


10207 


46534 


95 


2-58571 


38674 


1-48623 


1-00048 


46 


58.107 


63128 


10768 


47640 


96 


2-01170 


38289 


1-40729 


1-11440 


47 


59999 


62500 


11250 


48750 


97 


2-03794 


37008 


1-50851 


1-12043 


48 


01607 


61878 


11743 


49865 


98 


2-60446 


37531 


1-51988 


1-14457 


49 


1-63232 


61263 


12247 


50985 


99 


2-69123 


37158 


1-53141 


1-15083 


60 


1-61872 


60653 


1-12763 


52110 


I'OO 


2-71828 


36788 


1-51308 


1-17520 


















i 





EXPONENTIAL AND HYPERBOLIC FUNCTIONS continued. 



X 





-* 


COSH x 


SiNH X 


X 


e* 


-* 


COSH x 


SIXH x 


I'OO 


2-71828 


36788 


1-54308 


1-17520 


1-50 


4-48169 


22313 


2-35241 


2-12928 


roi 


2-74560 


36422 


1-55491 


1-19069 


1-51 


4-52673 


22091 


2-37382 


2-15291 


roa 


2-77319 


36059 


1-56689 


1-20630 


1-52 


4-57223 


21871 


2*39547 


2-17676 


1-03 


2-80107 


35701 


1-57904 


1-22203 


1-53 


4-61818 


21654 


2-41736 


2-20082 


1*04 


2-82922 


35345 


1*59134 


1-23788 


1-54 


4-66459 


21438 


2-43949 


2-22510 


















t 




1-05 


2-85765 


34994 


1-60379 


1-2538C 


1-55 


4-71147 


21225 


2-46186 


2-24961 


1-06 


2-88637 


34646 


1-61641 


1-26996 


1-56 


4-75882 


21014 


2-48 J48 


2-27434 


1-07 


2-91538 


34301 


1-62919 


1-28619 


1-57 


4-80665 


20805 


2-50735 


2-29930 


1-08 


2-94-168 


33960 


1-64214 


1-30254 


1-58 


4-85496 


20598 


2-53047 


2-32449 


1-08 


2-97427 


33622 


1-65525 


1-31903 


1-59 


4-90375 


20393 


2-65384 


2-34991 


no 


3-00417 


33287 


1-66852 


1-33565 


1-60 


4-95303 


20190 


2-67746 


2-37567 


rn 


3-03436 


32956 


1-68196 


1-35240 


1-61 


5-00281 


19989 


2-60135 


2-40146 


ria 


3-06485 


32628 


1-69557 


1-36929 


1-62 


5-05309 


19790 


2-62549 


2-42760 


ris 


3-09566 


32303 


1-70934 


1-38631 


1-63 


5-103H7 


19593 


2-64990 


2-45397 


ri4 


3-12677 


31982 


1-72329 


1-40347 


1-64 


5-15517 


19398 


2-67457 


2-48059 


ris 


3-15819 


31664 


1-73741 


1-42078 


1-66 


5-20698 


19205 


2-69951 


2-50746 


rie 


3-18993 


31349 


1-75171 


1-43822 


1-66 


5-25931 


19014 


2-72472 


2-53459 


ri7 


3-22199 


31037 


1-76618 


1-45581 


1-67 


5-31217 


18825 


2-75021 


2-56196 


ris 


3-25437 


30728 


1-78083 


1-47355 


1-68 


5-36556 


18637 


2-77696 


2-58959 


ri9 


3-28708 


30422 


1-79565 


1-49143 


1-69 


5-41948 


18452 


2-80200 


2-61748 


1*20 


3-32012 


30119 


1-81006 


1-50946 


1-70 


5-47395 


18268 


2-82832 


2-64563 


1-21 


3-35348 


29820 


1-82584 


1-52764 


T71 


5-52896 


18087 


2-85491 


2-67405 


1-22 


3-38719 


29523 


1-84121 


1-54598 


1-72 


6-58453 


17907 


2-88180 


2-70273 


1-23 


3-42123 


29229 


1-85676 


1-56447 


1*73 


6-64065 


17728 


2-90897 


2-73168 


1*24 


3-45561 


28938 


1-87250 


1-58311 


1-74 


5-69734 


17552 


2-93643 


2-76091 


1-25 


3-49034 


28650 


1-88842 


1-60192 


1-75 


5-75460 


17377 


2-96419 


2-79041 


1-28 


9-52542 


28365 


1-90454 


1-62088 


1-78 


5-81244 


17204 


2-99224 


2-82020 


1-27 


3-56085 


280.S3 


1-92084 


1-64001 


1-77 


5-87085 


17033 


3-02059 


2-85026 


1-28 


3-50664 


27804 


1-93734 


1-65930 


1-78 


5-92986 


16864 


3-04925 


2-83061 


1-29 


d-63279 


27527 


1-95403 


1-67870 


1-79 


5-98946 


16696 


3-07821 


2-91125 


1-30 


3-66930 


27253 


1-97091 


1-69838 


1-80 


6-04965 


16530 


3-10747 


2-94217 


1-31 


3-70617 


2(5982 


1-98800 


1-71818 


1-81 


6-11045 


16365 


8-13705 


2-97340 


1'32 


3-74342 


26714 


2-00528 


1-73814 


1*82 


6-17186 


16203 


3-16694 


3-00492 


1-33 


3-78104 


26448 


2-02276 


1-76828 


1'83 


6-23389 


16041 


3' 197 15 


4-03674 


1-34 


3-81904 


26185 


2-04044 


1-77860 


1-84 


6-29654 


15882 


3'22768 


3*06886 


1-35 


3-85743 


-25924 


2-05833 


1-79909 


1*85 


6-35982 


15724 


3'25853 


3-10129 


1-36 


3-89619 


25666 


2-07643 


1-81977 


1'86 


i-42374 


16567 


3-28970 


3-13403 


1-37 


3-93535 


25411 


2-09473 


1-84062 


1*87 


6-48830 


15412 


3-32121 


3-16709 


1-38 


3-97490 


25158 


2-11324 


1-86166 


1-88 


6-55350 


15259 


3-35305 


3-20046 


1-39 


4-01485 


24908 


2-13196 


1-88289 


1-89 


6-61937 


15107 


3-38522 


3-23415 


T40 


4-05520 


24660 


2-15090 


1-90430 


1-90 


6-68589 


14957 


3-41773 


3-26816 


1'41 


4-0959G 


24414 


2-17005 


1-92591 


T91 


6-76309 


14808 


3'4f)058 


d-30250 


1-42 


4-13712 


24171 


2-18942 


1-94770 


1-92 


6-82096 


14661 


3-48378 


3-33718 


1-43 


4-17870 


23931 


2-20900 


1-96970 


1-93 


6-88951 


14515 


3-51733 


3-37218 


1*44 


4-22070 


23693 


2-22881 


1-99188 


1'94 


6-95875 


14370 


3-55123 


3-40752 


1-45 


4-26311 


23457 


2-24884 


2-01428 


1-95 


7*02869 


14227 


3-58548 


3-44321 


1-46 


4-30596 


23224 


2-26910 


2-03686 


1-96 


7-09933 


14086 


3-62009 


3-47923 


1-47 


4-34924 


22993 


2-28958 


2-05965 


1-97 


7-17068 


13946 


3-65507 


3-51561 


1*48 


4-39295 


22764 


2-31029 


2-08265 


1*98 


7-24274 


13807 


3-69011 


3-55234 


1-49 


4-43710 


22537 


2-33123 


2-10586 


1'99 


7-31553 


13670 


3-72611 


3-58942 


1*50 


4-48169 


22313 


2-35241 


2-12928 


2-00 


7-38906 


13634 


3-76220 


3-62686 



66 



EXPONENTIAL AND HYPERBOLIC FUNCTIONS -continued. 



X 


e* 


-* 


Cos u x 


SIKH x 


x 


t* 


e-* 


COSHZ 


SlXH X 


2'0 


7-38906 


13534 


3-76220 


3-62686 


4'0 


54-5982 


01832 


27-3082 


27-2899 


2*1 


8-16617 


12246 


4-14431 


4-02186 


41 


60-3403 


01657 


30-1784 


30-1619 


2*2 


0-02501 


11080 


4'5679l 


4-45711 


4*2 


66-6863 


01500 


33-3507 


33-3357 


2*3 


9-97418 


10026 


5-03722 


4-93096 


4*3 


73-6998 


01357 


36-8567 


36-8431 


2*4 


11-0232 


09072 


6-66695 


6-46623 


4*4 


81-4509 


01228 


40-7316 


40-7193 


2'5 


12-1825 


08208 


6-13229 


6-05020 


4'5 


90-0171 


01111 


45-0111 


45-0030 


2*6 


18-4637 


07427 


6-76900 


6-69473 


4'6 


99-4843 


01005 


49-7472 


49-7371 


2'7 


14-8797 


0672L 


7-47347 


7-40626 


4'7 


109-947 


00910 


54-9781 


54-9690 


2*8 


16-4446 


06081 


8-25273 


8-19192 


4'8 


121-510 


00823 


60-7593 


60-7511 


2*9 


18-1741 


05502 


9-11458 


9-05956 


4*9 


134-290 


00745 


67-1486 


67-1412 


3'0 


20-0855 


04979 


10-0677 


10-0179 


6'0 


148-413 


00674 


74-2099 


74-2032 


3'1 


22-1980 


04505 


1M215 


11-0765 


51 


164-022 


00610 


82-0140 


82-0079 


3'2 


24-5325 


04076 


12-2866 


12-2459 


5*2 


181-272 


00552 


90-6388 


90-6333 


3'3 


27-1126 


03688 


13-5747 


13-6379 


5'3 


200-337 


00499 


100-171 


100-167 


3*4 


29-9641 


03337 


14-9987 


14-9654 


5*4 


221-406 


00452 


110-705 


110-701 


3'6 


33-1155 


03020 


16-5728 


16-5426 


5'5 


244-692 


00409 


122-348 


122-344 


3'8 


36-5982 


02732 


18-3128 


18-2855 


5-8 


270-426 


00370 


135-215 


135-211 


3*7 


40-4473 


02472 


20-2360 


20-2113 


6'7 


298-867 


00335 


149-435 


149-432 


3'8 


44-7012 


02237 


22-3618 


22-3394 


5'8 


330-300 


00303 


165-151 


165-148 


3'9 


49-4021 


02024 


24-7113 


24-6911 


5'9 


365-037 


00274 


182-520 


182-517 


4*0 


54-5982 


01832 


27-3082 


27-2899 


8'0 


403-429 


00248 


201-716 


201-713 



XXII.-Loo w ' 



X 





1 


2 


3 


4 


5 


8 


7 


8 


9 


1 


43429 


47772 


52115 


56458 


60801 


65144 


69487 


73830 


78173 


82516 


2 


86859 


91202 


95545 


99888 


1-04231 


1-08574 


1-12917 


1-17260 


1-21602 


1-25945 


3 


1-30288 


1 -34631 


1-38974 


1-43317 


1 '47600 


1-62003 


1-56346 


1-60689 


1-05032 


1-69375 


4 


1*73718 


1-78061 


1-82404 


1-86747 


1-91090 


1-95433 


1-99775 


2-04118 


2-08461 


2-12804 


6 


2-17147 


2-21490 


2-25833 


2-30176 


2-34519 


2-388G2 


2-43205 


2-47548 


2-61891 


2-56234 


6 


2-60577 


2-64920 


2-69263 


2-73006 


2-77948 


2-82291 


2-86634 


2-90977 


2-95320 


2-99663 


7 


3-04006 


3-08349 


3-12692 


8-17035 


3-21378 


3-25721 


3-30064 


3-34407 


3-38760 


3-43093 


8 


3*47436 


3-51779 


3-56121 


3-60464 


3-64807 


3-69150 


3-73493 


3-77836 


3-82179 


3-86522 


9 


3-90865 


3-95208 


3-99551 


4-03894 


4-08237 


4-12580 


4-16923 


4-21266 


4-25609 


4-29952 


10 


4-84294 






















01 


02 


03 


04 


05 


08 


07 


08 


09 


DIFFERENCES 


434 


809 


1303 


1737 


2171 


2C06 


3040 


3474 


3909 



XXIII. = (LOO. TAN ^45 + f)) =3-<f- l 



* 


N 


* 


u 





u 


* 


u 







o 




o 




o 




o-o 


00000 


22'5 


40320 


45-0 


88137 


67'6 


1*61489 


0'5 


00873 


23-0 


41206 


45-5 


89377 


68*0 


1-63794 


ro 


01745 


23*5 


42216 


46'0 


90628 


68-6 


1-66148 


T5 


02618 


24-0 


43169 


46'5 


91890 


69-0 


1-68557 


2-0 


03491 


24*5 


44127 


47-0 


93163 


69*5 


1*71020 


2'5 


043G5 


25'0 


45088 


47'5 


94449 


70-0 


1-73542 


3-0 


05238 


25'5 


46052 


48'0 


95747 


70-5 


1*76124 


3'5 


06112 


26-0 


47021 


48'5 


97057 


71'0 


1-78771 


4'0 


OG987 


26'5 


47994 


49*0 


98381 


71'5 


1-81486 


4'5 


07862 


27'0 


48972 


49*5 


99718 


72-0 


1-84273 


5*0 


08738 


27'5 


49953 


50'0 


1-01068 


72*5 


1-87136 


6'5 


09614 


28'0 


50939 


50-5 


02133 


73-0 


1'90079 


6-0 


10491 


28'5 


51930 


51'0 


03812 


73'5 


1-93107 


6*5 


11369 


29*0 


52925 


51*5 


05207 


74*0 


1-96226 


7'0 


12248 


29'5 


53925 


52'0 


06616 


74*5 


1-99441 


7'5 


13128 


30*0 


54931 


62-5 


08042 


75'0 


2-02769 


8-0 


14008 


30*5 


55941 


63*0 


09483 


75'5 


2-06187 


8'5 


14890 


31-0 


56956 


53*5 


10942 


76-0 


2-09732 


9'0 


15773 


31-5 


57977 


64-0 


12418 


76'5 


2-13404 


9'5 


16657 


32-0 


59003 


54-5 


13911 


77-0 


2-17212 


10-0 


17543 


32-5 


60035 


65-0 


15423 


77'5 


2-21167 


10-5 


18429 


33-0 


61073 


55-5 


16954 


78*0 


2-25280 


iro 


19318 


33-5 


62116 


56-0 


18505 


78'5 


2-29566 


11-6 


20207 


34-0 


63166 


56-5 


20076 


79-0 


2-34040 


12'0 


21099 


34-5 


64222 


57-0 


21667 


79'5 


2-38719 


12-5 


21992 


35-0 


65284 


67-6 


23281 


80'0 


2-43625 


13-0 


22886 


35'5 


66352 


58'0 


24916 


80'5 


2-48779 


13'5 


23783 


36-0 


67428 


68'5 


1-20574 


81'0 


2-64209 


14'0 


24681 


36-5 


68510 


69-0 


1-28257 


81-5 


2-69947 


14'5 


25582 


37-0 


69599 


59-5 


1-29963 


82'0 


2-66031 


15-0 


26484 


37'5 


70695 


80-0 


1-31696 


82'5 


2-72501 


15-5 


27389 


38'0 


71799 


60-5 


1-33454 


83'0 


2-79422 


16-0 


28295 


38'5 


72910 


61-0 


1-35210 


83'5 


2-86850 


16'5 


29204 


39-0 


74029 


61-6 


1-37055 


84-0 


2-94870 


17'0 


30116 


39'5 


75156 


62-0 


1-38899 


84'6 


3-03586 


17'5 


31030 


40'0 


76291 


62'5 


1-40773 


86-0 


3-13130 


18-0 


31946 


40*5 


77434 


63-0 


1-42079 


855 


3-23678 


18*5 


32865 


41*0 


78586 


63-5 


1-44618 


86-0 


3-35467 


19'0 


33786 


41-6 


79747 


64-0 


1-46591 


86*5 


3-48830 


19-5 


34711 


42*0 


80917 


64'5 


1-48600 


87'0 


3-64253 


20-0 


35638 


42'5 


82096 


65-0 


1-50645 


87*5 


3-82492 


20-5 


36568 


43-0 


83284 


65'5 


1-52730 


88-0 


4-04813 


21-0 


37501 


43'5 


84482 


66*0 


1-54855 


88*5 


4-33585 


21'5 


38438 


44-0 


85690 


66*5 


1-57022 


89*0 


4-74135 


220 


39377 


44*5 


86909 


67-0 


1*69232 


89'5 


5-43451 














90*0 


Inf. 



6S 



XXIV. ELLIPTIC 



* 


= 


= 50 


= 10 


= 15 


= 20 


= 25 


= 30 


= 35 


= 40 C 


= 45 


1 


01745 


01745 


01745 


01745 


01745 


01745 


01745 


01745 


01745 


01745 


a 


03491 


03491 


03491 


03491 


03491 


03491 


03491 


03491 


03491 


03491 


3 


05230 


05236 


05230 


05236 


05236 


05236 


05237 


05237 


05237 


05237 


4 


00981 


06981 


00981 


06982 


06982 


06982 


OC!)83 


06983 


06984 


06984 


5 


08727 


08727 


08727 


08727 


08728 


08729 


08729 


08730 


08731 


08732 


6 


104/2 


10472 


10473 


10473 


10474 


10475 


10477 


10478 


10480 


10482 


7 


12217 


12218 


12218 


12219 


12221 


12223 


12225 


12227 


12230 


12233 


8 


13963 


13963 


13904 


1390G 


13968 


13971 


13974 


13978 


13981 


13985 


9 


16708 


15708 


15710 


15712 


15715 


15719 


15724 


15729 


15735 


15740 


10 


17453 


17454 


17456 


17459 


17464 


17409 


17475 


17482 


17490 


17498 


11 


19199 


19200 


19202 


19206 


19212 


19220 


19228 


19237 


19247 


19258 


12 


20944 


20945 


"2094!) 


20954 


20962 


201)71 


20982 


20994 


21007 


21021 


13 


22G8!) 


22691 


220D5 


22702 


22712 


22724 


22738 


22753 


22770 


22787 


14 


24435 


24436 


24442 


24451 


24403 


24478 


24495 


24514 


24535 


24556 


15 


2G180 


26182 


26189 


26200 


20215 


26233 


26254 


26278 


20303 


26330 


16 


27925 


27928 


27936 


27949 


27967 


27989 


28015 


28044 


28075 


28107 


17 


29671 


29674 


29081 


29699 


29721 


21)748 


29779 


29813 


29850 


29889 


18 


31416 


31420 


3i4:u 


31450 


31475 


31507 


31544 


31585 


31629 


31675 


10 


33161 


33166 


33179 


33201 


33231 


33208 


33312 


33300 


33412 


3.'I4 66 


20 


34907 


34912 


34927 


34953 


34988 


35031 


35082 


35138 


35199 


35262 


21 


36652 


36658 


36676 


36706 


30746 


30796 


36855 


36920 


36990 


37063 


22 


38397 


38404 


38425 


38459 


38505 


38563 


38630 


38705 


38786 


38871 


23 


40143 


40151 


40174 


40213 


40200 


40331 


40408 


40494 


.40587 


40683 


24 


41888 


41897 


41924 


41908 


42027 


42102 


421H9 


42287 


42392 


42503 


25 


43633 


43643 


43674 


43723 


43791 


43875 


43973 


44081 


44203 


44328 


26 


45379 


45390 


45424 


45479 


45555 


45650 


45761 


45885 


46020 


46161 


27 


47124 


47137 


47174 


47230 


47321 


47427 


47551 


47090 


47841 


48000 


28 


48869 


48883 


48925 


48994 


49089 


49207 


49345 


49500 


49069 


49840 


29 


50615 


50630 


50677 


50753 


50858 


50988 


51142 


51315 


51503 


51700 


30 


52360 


52377 


62428 


52513 


52628 


52773 


52943 


53134 


53343 


53562 


31 


54105 


54124 


'54181 


54273 


54401 


54560 


54747 


54959 


56189 


55432 


32 


55851 


55871 


55933 


50035 


56175 


56349 


56555 


56788 


57042 


57310 


33 


57596 


57619 


57686 


57797 


57950 


58141 


58367 


58623 


58902 


69197 


34 


59341 


69366 


59439 


59501 


59727 


59936 


60183 


00463 


60769 


61093 


35 


61087 


61113 


61193 


61325 


61506 


61734 


62003 


62308 


62643 


62998 


36 


62832 


62861 


62948 


63090 


63287 


63534 


63827 


64159 


64524 


64912 


37 


64577 


04609 


64702 


64857 


65070 


65337 


65655 


66016 


66413 


66836 


38 


66323 


66356 


66457 


60624 


6G854 


67144 


67487 


07879 


68309 


68769 


39 


C8068 


68104 


68213 


68393 


68641 


68953 


69324 


69747 


70214 


70713 


40 


69813 


69852 


69969 


70162 


70429 


70765 


71165 


71622 


72126 


72667 


41 


71558 


71600 


71726 


71933 


72219 


72680 


73010 


73502 


74047 


74632 


42 


73304 


73349 


73483 


73704 


74011 


74398 


74860 


75389 


75976 


76608 


43 


76049 


75097 


75240 


75477 


75805 


76219 


76714 


77282 


77914 


78594 


44 


76794 


76846 


70998 


77251 


77600 


78013 


78573 


79182 


79860 


80592 


45 


78540 


78594 


78756 


79026 


79398 


79871 


80437 


81088 


81815 


82302 



FUNCTIONS. F(0, 



69 



<9 = 50 


= 65 


</ = 60 


4 = 65 


= 70 


= 75 


* = 80 


= 85 


o = 9<)o 


* 


01745 


01745 


01745 


01745 


01745 


01745 


01745 


01745 


01745 


1 


03491 


03491 


03491 


03491 


03491 


03491 


03491 


03491 


03491 


2 


05237 


05238 


05238 


05238 


05238 


05238 


05238 


05238 


05*238 


3 


06985 


06985 


06986 


00986 


06986 


0(5987 


06987 


00987 


00987 


4 


08733 


08734 


08735 


08736 


08736 


08737 


08737 


08738 


08738 


5 


10483 


10485 


10486 


10488 


10489 


10190 


10491 


10491 


10491 


6 


12235 


12238 


12240 


12242 


12244 


122 10 


12247 


12218 


12218 


7 


13989 


13993 


13997 


14000 


14003 


J 100.") 


14007 


14008 


14008 


8 


15746 


15751 


15757 


15761 


15705 


15709 


15771 


15772 


15773 


9 


17605 


17513 


17520 


17526 


17532 


17537 


17540 


17542 


17513 


10 


19268 


19278 


19288 


19296 


19301 


19310 


19314 


19317 


19318 


11 


21034 


21047 


21059 


"21071 


21080 


2 loss 


21094 


21098 


21099 


12 


22801 


22821 


22K30 


22851 


22803 


22873 


22HHO 


22885 


2'286 


13 


24578 


24599 


2401 8 


24030 


24052 


21001 


24074 


24(580 


24(581 


14 


26356 


26382 


26406 


20428 


20448 


20403 


26475 


20482 


20484 


16 


28139 


28171 


28200 


28227 


28251 


28270 


28284 


28293 


28295 


16 


29927 


29.%5 


30001 


MOM 


30002 


300H, r > 


30102 


30112 


30110 


17 


31721 


31706 


31809 


3184H 


31881 


31900 


31929 


31942 


31946 


18 


33520 


33574 


33624 


33070 


33710 


33712 


33706 


33781 


33786 


19 


35326 


35388 


35447 


35501 


35548 


3558(5 


35615 


35032 


36638 


20 


37137 


'.37210 


37279 


37342 


373%' 


3744 1 


37474 


37494 


37501 


21 


38956 


31KHO 


39119 


39192 


39255 


39307 


39346 


393(59 


39377 


22 


40782 


40878 


40909 


41053 


41120 


411X0 


41230 


41257 


41200 


23 


42614 


42724 


42829 


42925 


43008 


43077 


43128 


43159 


43109 


24 


44455 


44580 


44099 


44808 


44904 


44982 


45040 


45075 


45088 


25 


46304 


46445 


46580 


46704 


46812 


46901 


46967 


47008 


47021 


26 


48161 


48320 


48472 


48012 


48735 


48835 


48910 


48956 


48972 


27 


50027 


50206 


30377 


50534 


50072 


507H5 


50870 


50922 


50939 


28 


51902 


52102 


52293 


52470 


52024 


52752 


52847 


52905 


52925 


29 


53787 


54009 


64223 


54420 


54593 


54736 


54843 


54908 


54931 


30 


55681 


55928 


56166 


56386 


50579 


56739 


56858 


56931 


56966 


31 


57586 


57860 


58123 


58367 


58582 


58700 


58893 


58975 


59003 


32 


59501 


59803 


60095 


60305 


60604 


GOS02 


00950 


61042 


61073 


33 


61427 


61760 


02082 


62381 


62646 


62865 


63029 


03131 


63166 


34 


63364 


63730 


64085 


64415 


64707 


64950 


65132 


65245 


6*284 


35 


65313 


65715 


66104 


66468 


66790 


67058 


67260 


67386 


67428 


36 


67273 


67713 


68141 


G8540 


68895 


69191 


69414 


69562 


69599 


37 


69246 


69727 


70195 


70633 


71023 


71349 


71594 


71747 


71799 


38 


71232 


71756 


72267 


72746 


73175 


73. r )33 


73804 


73972 


740'29 


39 


73231 


73801 


74358 


74882 


'75352 


75745 


76043 


76228 


76291 


40 


76243 


^75862 


76469 


77041 


77555 


77987 


78313 


78517 


78586 


41 


77269 


77940 


78600 


79224 


79786 


80258 


80617 


80841 


80917 


42 


79308 


80035 


80752 


81432 


82045 


82562 


82954 


83200 


83284 


43 


81362 


82149 


82926 


83665 


84333 


84898 


85329 


85598 


85690 


44 


83431 


84281 


85122 


85925 


86053 


87270 


87741 


88037 


88137 


45 












i 







ELLIPTIC FUNCTIONS, 



* 


= 


= 5 


3 = 10 


= 15 


= 20 


= 25 


= 30 


= 35 


= 40 


= 450 


46 


80285 


80343 


80515 


80801 


81198 


81701 


82305 


83001 


83779 


84623 


47 


82030 


82092 


82275 


82578 


82999 


83535 


84178 


8-1920 


85752 


86656 


48 


83776 


83841 


84035 


84356 


84803 


85371 


86065 


86846 


87734 


88701 


49 


85521 


85590 


85795 


86135 


86609 


87211 


87937 


88779 


89725 


90759 


60 


872G6 


87339 


87556 


87915 


88416 


89054 


89825 


90719 


91725 


92829 


51 


89012 


89088 


89317 


896.07 


D0226 


90901 


91716 


92CG5 


93735 


94912 


52 


90757 


90838 


91078 


91479 


92037 


92750 


93613 


94618 


95755 


97007 


53 


92502 


92587 


92841 


93262 


93850 


94603 


95514 


96578 


97784 


99115 


54 


94248 


91337 


94003 


95047 


95666 


96458 


97420 


98545 


99822 


1-01237 


55 


95993 


96086 


96366 


96832 


97483 


98317 


99331 


1-00519 


1-01871 


1-03371 


56 


97738 


97836 


98130 


98618 


99302 


1-00179 


1-01247 


1-02499 


1-03928 


1-05519 


57 


99484 


99586 


99894 


1-00406 


1-01123 


1-02044 


1-03167 


1-04487 


1-05996 


1-07680 


58 


1 '01 229 


1-01336 


1-01658 


1-02194 


1-02946 


1-03912 


1-05092 


1-06481 


1-08073 


1-09854 


59 


1-02974 


1-03086 


1-03423 


1-03981 


1-04770 


1-05783 


1-07021 


1-08482 


1-10159 


1-12042 


60 


1*04720 


1-04837 


1-05188 


1-05774 


1-06597 


1-07657 


1-08955 


1-10190 


1-12256 


1-14243 


61 


1-06465 


1-06587 


1-06954 


1-07566 


1-08425 


1-09534 


1-10894 


1-12504 


1-14361 


1-16457 


62 


1-08210 


1-OH338 


1-08720 


1-09358 


1-10255 


1-11414 


1-12837 


1-14525 


1-16476 


1-18685 


63 


! 09956 


1-10088 


10486 


1-11151 


1-12087 


1-13296 


1-14784 


1-16552 


1-18601 


1-20926 


64 


1-11701 


1-118:59 


12253 


1-12945 


1-13920 


1-15182 


1-16735 


1-18586 


1-20735 


1-23180 


65 


1-13446 


1-13590 


14020 


1-14740 


1-15755 


1-17070 


1-18691 


1-20626 


1-22877 


1-25447 


66 


1-15192 


1-15340 


15787 


1-16536 


1-17592 


1-18961 


1-20651 


1-22672 


1-25029 


1-27727 


67 


1*16937 


1-17091 


17555 


1-18333 


1- 194I50 


1-20854 


1-22615 


1-24724 


1-27190 


1-30020 


68 


1-18(582 


1-18842 


19324 


1-20130 


1-212(59 


1-22750 


1-24583 


1-26782 


l-29,'559 


1-32325 


69 


1-20428 


1-20593 


1-21002 


1-21928 


1-23110 


1-24648 


1-26555 


1-28846 


1-31537 


1-34642 


70 


1-22173 


1-22345 


1-22861 


1-23727 


1-24953 


1-26548 


1-28530 


1-30915 


1-33723 


1-36972 


71 


1-23918 


1-24096 


1-24630 


1-25527 


1-26796 


1-28451 


1-30509 


1-32990 


1-35917 


1-39313 


72 


1 '26664 


1-25847 


1-26400 


1-27328 


1-28641 


1-30356 


1-32491 


1-35070 


1-38118 


1-41666 


73 


1-27409 


1-27599 


1-28169 


1-29129 


1-30488 


1-32263 


1-34477 


1-371,* 5 


1-40328 


44030 


74 


1-29154 


1-29350 


1-29939 


1-30930 


1-32335 


1-34172 


1-36466 


1-39244 


1-42544 


46404 


75 


1-3U900 


1-31102 


1-31710 


1-32733 


1-34184 


1-36083 


1-38457 


1-41339 


1-44767 


1-48788 


76 


1-32645 


1-32853 


1-33480 


1-31535 


1-36034 


1-37996 


1-40452 


1-43437 


1-46997 


61183 


77 


1-34390 


1-34605 


1-35251 


1-36339 


1-37884 


1-39911 


1-42449 


1-45540 


1-49232 


53586 


78 


1-3G136 


1-30356 


1-37022 


1-38143 


1-39736 


1-41827 


1-44449 


1-47647 


1-51474 


55999 


79 


1-37881 


1-38108 


1-38793 


1-39947 


1-41588 


1-43744 


1-46151 


1-49757 


1-53721 


1-58419 


80 


1-39626 


1-39860 


1-40565 


1-41752 


1-43442 


1-456G3 


1-48455 


1-51870 


1-55973 


1-60848 


81 


1-41372 


1-41612 


1-42336 


1-43557 


1-45296 


1-47583 


1-50462 


1-53987 


1-58230 


1-63283 


82 


1-43117 


1-43364 


1-41108 


1-45362 


1-47150 


1-49504 


1-52470 


1-56106 


1-60491 


1-65725 


83 


1-44862 


1-45115 


1-45879 


1-47168 


1-49005 


1-51426 


1-54479 


1-58228 


1-62756 


1-68172 


84 


1-4G608 


1-46867 


1-47651 


1-48974 


1-50861 


1-53350 


1-56490 


1-60352 


1-65024 


1-70(525 


85 


1-48353 


1*48619 


1-49423 


1-50781 


1-52717 


1-65273 


1-58503 


1-62478 


1-67295 


1-73082 


86 


1-50098 


1-50371 


1-51195 


1-52587 


1-54574 


1-57198 


1'60516 


1-64605 


1*69569 


1-75542 


87 


1-51844 


1-52123 


1-52968 


1-54394 


1-56431 


1-59123 


1-62530 


1-66734 


1*71844 


1-78006 


88 


1-53589 


1-53875 


1-54740 


1-56200 


1-58288 


1-61048 


1-64545 


1-68864 


1-74121 


1-80472 


89 


1-65334 


1-55627 


1-56512 


1-58007 


1-60145 


1-62974 


1-66560 


1'70994 


1*76399 


1-82939 


90 


1-57080 


1-57379 


1-58284 


1-59814 


1-62003 


1-64900 


1-68575 


1*73125 


1*78677 


1-85407 



0, $) continued. 



* = 50 


= 55 


= 60 


= 65 


0=70 


= 75 


<? = 80 


' = 85 


o = 90 


+ 


'85515 


86431 


87342 


88213 


89005 


89678 


90193 


90517 


90628 


46 


870 14 


88601 


89585 


90529 


91390 


92124 


92(587 


93042 


931G3 


47 


89729 


90791 


91853 


92875 


93811 


94610 


95226 


95614 


95747 


48 


91860 


93001 


94146 


95252 


96267 


97139 


97810 


98235 


98381 


49 


94008 


95232 


96465 


97660 


98762 


99711 


1-00444 


1-00909 


1-01.068 


50 


96171 


C7<*84 


98811 


1-00102 


1-01297 


1-02329 


1-03129 


1-03638 


1-08812 


61 


98352 


99709 


1-01185 


1-02578 


1-03872 


1-04995 


1-05868 


1-06425 


1-00010 


52 


1-00550 


1-02055 


1-03587 


1 '05089 


1-06491 


1-07711 


1-08665 


1-09274 


1-09183 


53 


1-02765 


1-04374 


1-06018 


1-07637 


1-09155 


1-10481 


1-11521 


1-12188 


1-12118 


54 


1-04998 


1-06716 


1-08479 


1-10223 


1-11865 


1-13307 


1-14442 


1-15171 


1-15423 


55 


1-07248 


1-09082 


1-10971 


1-12848 


1-14624 


1-16190 


1-17430 


1-18229 


1-18505 


56 


09517 


1-11472 


1-13494 


1-15513 


1-17433 


19136 


1-20488 


1-21364 


1-21067 


57 


11803 


1-13886 


! 16050 


1-18220 


1-20295 


22145 


1-23G23 


1-24582 


1-24916 


58 


14108 


1-16325 


P1H638 


1-20970 


1-23212 


25223 


1-26837 


1-27890 


1-28267 


59 


16432 


1-18788 


1-21254 


1-23764 


1-26186 


28371 


1-30135 


1-31292 


1-31696 


60 


18773 


1-21277 


1-23916 


1-20604 


1-29219 


31594 


1-33524 


1-34795 


1-35240 


61 


21134 


1-23792 


1-26606 


1-2IM90 


1-32314 


34896 


1-37008 


1-38407 


1-38899 


62 


23513 


1-26332 


1-29332 


1-32425 


1-35473 


38281 


1-40594 


1-42135 


1-42079 


63 


25910 


1-28898 


1-32094 


1-35409 


1-38099 


41753 


1-44288 


1-45989 


1-46591 


64 


1-28326 


1-31491 


1-34893 


1-38443 


1-41994 


45316 


1-48098 


1-49977 


1-50645 


65 


1-30760 


1-34109 


1-37728 


1-41529 


1-45360 


48976 


1-52031 


1-54112 


1-54855 


66 


1-33212 


1-36753 


1-40600 


1-44668 


1-48800 


52738 


1-56096 


1-58404 


1-59232 


67 


1-35683 


39423 


1-43510 


1-47860 


1-52317 


5(1006 


1-C0303 


1-62868 


1-63794 


68 


1-38171 


42119 


1-46457 


1-51107 


1-55913 


(50586 


1-64661 


1-67518 


1-08557 


69 


1-40677 


1-44840 


1-49441 


1-54410 


1-59591 


64684 


1-69181 


1-72372 


1-73542 


70 


1-43200 


47587 


1-52463 


1-57768 


1-63352 


68905 


1-73877 


1-77450 


1-78771 


71 


1-45739 


50359 


1-55522 


1-61182 


1-67198 


73256 


1-78759 


1-82774 


1-84273 


72 


1-48296 


53155 


1-58618 


1-64653 


1-71132 


77743 


1-83844 


1-88370 


1-90079 


73 


1-50867 


55974 


1-01750 


1-68180 


1-75155 


82371 


1-89146 


1-94267 


1-90220 


74 


1-53455 


58817 


1-64918 


1-71763 


1-79269 


1-87145 


1-94682 


2-00499 


2-02759 


75 


1-56056 


1-61682 


1-68120 


1-75401 


1-83473 


1-92073 


2-00470 


2-07106 


2-09732 


76 


1-58672 


1-64569 


1-71356 


1-79094 


1-87768 


1-97157 


2-06529 


2-14136 


2-17212 


77 


1-61302 


1-67476 


1-74625 


1-82840 


1-92154 


2-02403 


2-12878 


2-21044 


2-25280 


78 


1-63943 


1-70403 


1-779-24 


1-86637 


1-96630 


2-07813 


2-19538 


2-29694 


2-J4040 


79 


1-66597 


1-73347 


1-81253 


1-90484 


2-01193 


2-13390 


2-26527 


2-38365 


2-43625 


80 


1-69261 


76309 


1-84609 


1-94377 


2-05840 


2-19131 


2-33866 


2-47748 


2-51209 


81 


1-71935 


79286 


1-87'.91 


1-98313 


2-10568 


2-25035 


2-41569 


2-57954 


2-66031 


62 


1-74618 


82278 


1-91395 


2-02290 


2-15371 


2-31097 


2-49648 


2-69109 


2-79422 


83 


1-77309 


85281 


1-94821 


2-06.J03 


2-20244 


2-37309 


2-58105 


2-81362 


2-94870 


84 


1*80006 


88296 


1-98264 


2-10348 


2-25178 


2-43658 


2-66935 


2-94869 


3-13130 


85 


1-82710 


1-91320 


2-01723 


2-14421 


2-30166 


2-50129 


2-76116 


3-09782 


3-35467 


86 


1-85418 


1-94351 


2-05194 


2-18515 


2-35198 


2-56703 


2-85612 


3- 201 98 


3-04253 


87 


1-88129 


1-97388 


2-08674 


2-2-2627 


2-40265 


2- (53357 


2-95366 


3-44116 


4-04813 


88 


1-90843 


2-00429 


2-12161 


2-26750 


2-45354 


2-70068 


3-05304 


3-63279 


4-74135 


89 


1*93558 


2-03472 


2-15652 


2-30879 


2-50455 


2-76806 


3-15339 


3-83174 


Inf. 


90 























XXV.-ELLIPTIO 



* 


tf = 


e = b 


= 10 


= 15 


= 20 


= 25 


= 30. 


= 35 


= 40 


= 46 


1 


01745 


01745 


01745 


01745 


01745 


01745 


01745 


01745 


01745 


01745 


2 


03491 


03491 


03491 


03491 


03491 


03491 


03490 


03490 


03490 


03490 


3 


0523G 


05236 


05236 


05236 


05236 


05236 


05235 


05235 


05235 


05235 


4 


06981 


06981 


06981 


06981 


06981 


OG980 


OG980 


06979 


06979 


06078 


5 


08727 


08727 


08726 


08726 


08725 


08725 


08724 


08723 


08722 


08721 


6 


10472 


10472 


10471 


10471 


10470 


10469 


10467 


10466 


10464 


10462 


7 


12217 


12217 


12216 


12215 


12214 


12212 


12210 


12207 


12205 


12202 


8 


13963 


13962 


13961 


13960 


13957 


13955 


13951 


13948 


13944 


13940 


9 


15708 


15707 


15706 


15704 


15700 


15G9G 


15692 


15G87 


15681 


15676 


10 


17453 


17453 


17451 


17447 


17443 


17438 


17431 


17424 


17417 


17409 


11 


19199 


19198 


19195 


191JU 


19185 


19178 


191G9 


19160 


19150 


19140 


12 


20044 


20943 


20939 


20931 


20926 


20917 


20906 


20894 


20881 


20868 


13 


22(589 


22688 


22683 


22G76 


22667 


22G55 


22641 


22G26 


22609 


22593 


14 


244:15 


24433 


24427 


24419 


24406 


24392 


24374 


24355 


24335 


24314 


15 


2G180 


2G178 


26171 


2G160 


26145 


26127 


26106 


26083 


26058 


26032 


16 


27925 


27923 


27914 


27901 


27883 


27861 


27836 


27807 


27777 


27746 


17 


29671 


29(i67 


29058 


29642 


29620 


29594 


29563 


29529 


29493 


29455 


18 


31416 


31412 


31401 


31382 


31357 


31325 


31289 


31248 


31205 


31161 


19 


33161 


33157 


33143 


33121 


33092 


33055 


33012 


32965 


32914 


32862 


20 


34907 


34901 


34886 


34860 


34825 


34783 


34733 


34678 


34619 


34558 


21 


36652 


36646 


36628 


36598 


36558 


36509 


36451 


36387 


36319 


36249 


22 


88397 


38390 


38370 


3H33G 


3821)0 


38233 


38167 


38093 


38015 


37934 


23 


40143 


40135 


40111 


40073 


40020 


39955 


39880 


39796 


39707 


39614 


24 


41888 


41879 


41852 


41809 


41749 


41676 


41590 


41496 


41394 


41289 


25 


43633 


43G23 


43593 


43514 


43477 


43394 


43298 


43191 


43076 


42958 


26 


45379 


45367 


45333 


45278 


45203 


45110 


45002 


44882 


44753 


44620 


27 


47124 


47111 


47074 


47012 


46928 


46824 


46703 


46569 


46425 


4627G 


28 


48869 


48855 


48813 


48745 


48651 


48536 


48402 


48252 


48092 


47926 


29 


50615 


50599 


50553 


50477 


50373 


50245 


50097 


49931 


49753 


49569 


30 


62360 


52343 


52292 


52208 


52094 


51953 


51788 


51605 


51409 


51205 


31 


54105 


54086 


54030 


53938 


53813 


53657 


53476 


53275 


53059 


52834 


32 


55851 


55830 


55768 


55667 


55530 


553GO 


55161 


54940 


54703 


54456 


33 


57596 


57573 


57506 


57396 


57245 


57059 


56842 


56600 


56341 


56070 


84 


59341 


59317 


59243 


59123 


58959 


58756 


58520 


58256 


57972 


57677 


35 


01087 


61060 


60980 


60850 


60672 


60451 


60194 


69907 


59598 


59276 


36 


62832 


62803 


62716 


62575 


62382 


62143 


61864 


61552 


61217 


60868 


37 


64577 


64546 


64452 


64300 


64091 


63832 


63530 


63193 


G2830 


62451 


38 


66323 


66289 


66188 


66023 


65798 


65519 


65193 


64828 


64436 


64027 


39 


68068 


68081 


67923 


67746 


67503 


67203 


66851 


66459 


66035 


65594 


40 


69813 


69774 


69658 


69467 


69207 


68884 


68506 


68081 


67628 


67153 


41 


71553 


71517 


71392 


71188 


70909 


70562 


70157 


69703 


69214 


68703 


42 


73304 


73259 


73126 


72907 


72609 


72238 


71804 


71318 


70793 


70245 


43 


75049 


75001 


74859 


74626 


74307 


73910 


73446 


72927 


72365 


71778 


44 


76794 


76744 


76592 


76343 


76003 


75580 


75085 


74530 


73931 


73303 


46 


78540 


78486 


78324 


78059 


77697 


77247 


76720 


76128 


75489 


74819 



FUNCTIONS. E(0,</). 



73 



= 60 


0=65 


= 60 


= 65 


= 70 


= 75 


= 80 


= 86 


= 90 


* 


01745 


01745 


01745 


01745 


01745 


01745 


01745 


01745 


01745 


1 


03490 


03490 


03490 


03490 


03490 


03490 


03490 


03490 


03490 


2 


05235 


05234 


05234 


05'234 


05234 


05234 


05234 


05^234 


05234 


3 


06978 


06978 


06977 


06977 


OG976 


06976 


00976 


06076 


OG976 


4 


08720 


08719 


08718 


08718 


08717 


08716 


08716 


08716 


08716 


5 


10461 


10459 


10458 


104 50. 


10155 


10454 


10453 


10453 


10453 


6 


12199 


12197 


12195 


12192 


12190 


12189 


12188 


12187 


12187 


7 


13936 


1S932 


13929 


13925 


131)23 


13WO 


131)19 


13918 


'13917 


8 


16670 


166G5 


15(560 


16656 


15(551 


16618 


15(545 


15644 


15643 


9 


17401 


17394 


17387 


17381 


17375 


17371 


173G7 


173G5 


17365 


10 


19180 


19120 


19110 


19102 


19095 


19089 


19084 


19082 


19081 


11 


20855 


20842 


20830 


20819 


20809 


20801 


20796 


20792 


20791 


12 


22576 


22559 


22544 


22530 


22518 


22508 


22501 


22-197 


2*195 


13 


24293 


24272 


24253 


2423U 


24221 


24209 


24200 


24194 


24192 


14 


26006 


25981 


25957 


25936 


25917 


25902 


25891 


25884 


26882 


15 


27714 


27684 


27655 


27G29 


27G06 


27588 


27575 


27567 


27564 


16 


29418 


29381 


29347 


29315 


29288 


292G7 


29250 


29241 


29237 


17 


31116 


31073 


31032 


30995 


30963 


30937 


30!) 17 


30JKJG 


30902 


18 


82809 


32758 


32710 


32666 


32629 


32598 


32575 


32561 


32557 


19 


84496 


34437 


34381 


34330 


34286 


34250 


34224 


34207 


84202 


20 


36178 


36109 


3C044 


35985 


35934 


35892 


35862 


35843 


35837 


21 


87853 


37773 


37699 


37631 


37572 


37525 


37490 


37468 


37461 


22 


39521 


39431 


39345 


39268 


39201 


39146 


39106 


3 ( .)()8l 


39073 


23 


41183 


41080 


40983 


40895 


40819 


40757 


40711 


40G83 


40674 


24 


42838 


42722 


42612 


42513 


42426 


42356 


42304 


42273 


42262 


25 


44486 


44355 


44232 


44120 


44023 


43944 


43885 


438-19 


43837 


26 


46126 


45980 


45842 


45716 


45607 


45518 


45453 


45413 


45399 


27 


47759 


47695 


47441 


47301 


47180 


4 70S I 


47007 


46962 


4G947 


28 


49383 


49202 


49031 


48875 


48740 


48G29 


48548 


48498 


48481 


29 


61000 


50799 


50609 


50437 


60287 


50165 


50074 


50019 


50000 


30 


52608 


52386 


52177 


51986 


51821 


51686 


51586 


61525 


61504 


31 


54207 


53964 


53733 


53524 


53341 


53193 


53082 


53015 


52992 


32 


55798 


55531 


55278 


55048 


54848 


54684 


54563 


54489 


64464 


33 


67379 


57087 


56811 


56559 


5G340 


56161 


56028 


55947 


55919 


34 


58952 


58634 


58332 


58057 


67818 


57622 


57477 


57388 


67368 


35 


60515 


60169 


59841 


59541 


59280 


590G7 


58909 


58811 


58779 


36 


62068 


61693 


61337 


61011 


60727 


60495 


60323 


60217 


60182 


37 


63612 


63206 


62820 


62467 


62159 


61907 


61720 


61605 


61566 


38 


65146 


64707 


64290 


63908 


63574 


63302 


63099 


62974 


62932 


39 


66671 


66197 


65746 


65334 


64974 


64679 


64459 


64324 


64279 


40 


68185 


67675 


67189 


66745 


66356 


66038 


66801 


65655 


65606 


41 


69688 


69140 


68619 


68140 


67722 


67379 


67124 


66966 


66913 


42 


71182 


70594 


70034 


69520 


69070 


68701 


68426 


68257 


68200 


43 


72665 


72036 


71436 


70884 


70401 


70005 


69710 


69527 


69466 


44 


74137 


73465 


72822 


72232 


71715 


71289 


70972 


70777 


70711 


45 



74 



ELLIPTIC FUNCTIONS 



+ 


*=o 


* = 5<> 


= 10 


* = 15 


* = 20 


= 25 


= 30 


= 35 


* = 40 


= 45<> 


46 


80285 


80228 


80056 


79775 


79390 


78911 


78350 


77721 


77040 


76326 


47 


82030 


81969 


81787 


81489 


81081 


80573 


79977 


79308 


78584 


77824 


48 


83776 


83711 


83518 


83202 


82770 


82231 


81599 


80890 


80121 


79313 


49 


85521 


85453 


85249 


84914 


84457 


83887 


83217 


82466 


81651 


80794 


50 


87266 


87194 


86979 


86626 


86142 


85539 


84832 


84036 


83173 


82265 


51 


89012 


88936 


88709 


88336 


87826 


87189 


86442 


85601 


84689 


83728 


52 


90757 


90677 


90438 


90045 


89507 


88836 


88048 


87161 


86197 


85182 


53 


92502 


92418 


92166 


91753 


91187 


90481 


89650 


88715 


-87698 


86627 


64 


94248 


94159 


93895 


93460 


92865 


92122 


91248 


90264 


89193 


88063 


55 


95993 


95900 


95622 


95166 


94541 


93761 


92843 


91807 


90680 


89490 


56 


97738 


97641 


97350 


96872 


96216 


95397 


94433 


93345 


92160 


90908 


57 


99484 


99381 


99077 


98576 


97889 


97030 


96019 


94878 


93634 


92318 


58 


1-01220 


1-01122 


1 '00803 


1-00279 


99560 


9H061 


97602 


96405 


95100 


93719 


59 


1 '02974 


1-02863 


1-02529 


1-01981 


1 '01 229 


1-00289 


99180 


97928 


96560 


95111 


60 


1-04720 


1-04603 


1-04255 


1-03683 


1'02897 


1-01915 


1-00756 


99445 


98013 


96495 


61 


1*06465 


1-06343 


1-05980 


1-05383 


1-04563 


1-03538 


1-02327 


1-00957 


99460 


97871 


62 


1-08210 


1-08084 


1-07705 


1-07083 


1-06228 


1-05J5H 


1-03895 


1-02165 


1'00900 


99238 


68 


1-09956 


1-01)824 


1-09430 


1-08781 


1-07H91 


1-06776 


1-05459 


1-03967 


1-02334 


1-00598 


64 


1-11701 


1-11564 


1-11154 


1-10479 


1-09553 


1-08392 


1-07020 


1-05465 


1-03762 


1-01949 


65 


1-13446 


1-13304 


1-12878 


1-12176 


I '11213 


1-10005 


1-08577 


1-06958 


1-05183 


1-03293 


66 


1-15192 


15013 


14601 


1-13873 


12871 


1-11616 


1-10132 


1-08447 


1-06599 


1-04629 


67 


I'lliiW 


16783 


16324 


1-15568 


14529 


1-13225 


1-11683 


1-09932 


1-08009 


1-05957 


68 


1- 18(18-2 


18,") 23 


18047 


1-17263 


16186 


1-14832 


1-1.-5231 


1-11412 


1-09143 


1-07279 


69 


1-20428 


20202 


19769 


1-18957 


17839 


1-1 (.437 


1-14776 


1-12888 


1-10812 


1-08593 


70 


1-22173 


22002 


1-21491 


1-20650 


19493 


1-18040 


1-16318 


1-14360 


1-12205 


1-09901 


71 


1-23918 


23741 


23213 


1-22343 


21145 


1-19640 


1-17857 


1-15828 


1-13594 


1-11202 


72 


1-25664 


25481 


24935 


1-24034 


22796 


1-21239 


1-19391 


1-17293 


1-14977 


1-12497 


73 


1-27409 


27220 


20656 


1-25726 


24416 


1-22837 


1-20928 


1-18754 


1-16356 


1-13786 


74 


1-29154 


28959 


28377 


1-27417 


2(5094 


1-24132 


1-22459 


1-20211 


1-17731 


1-15068 


75 


1-30900 


1-30698 


30097 


1-29107 


27742 


1-26026 


1-23989 


1-21666 


1-19101 


M6346 


78 


1-32645 


1-32437 


1-31818 


1-30796 


29389 


1-27619 


1-25516 


1-23117 


1-20467 


M7618 


77 


1-34390 


1-34176 


1-33538 


1-32486 


31035 


1-29210 


1-27041 


1-24566 


1-21830 


1-18885 


78 


1-36136 


1-35915 


1-35258 


1-34174 


32G80 


1-30800 


1-28565 


1-26012 


1-23189 


1-20148 


79 


1-37881 


1-37654 


1-36978 


1-35862 


34325 


1-32389 


1-30086 


1-27456 


1-24544 


1-21407 


80 


1-39626 


1-39393 


1-38698 


1-37550 


35968 


1-33976 


1-31606 


1-28897 


1-25897 


1-22661 


81 


1-41372 


1-41132 


1-40417 


1-39238 


1-37611 


1-35563 


1-33124 


1-30336 


1-27246 


1-23912 


82 


1-43117 


1-42871 


1-42137 


1-40925 


1-39254 


1-37148 


1-34641 


1-31773 


1-28594 


1-25159 


83 


1-44862 


1-44610 


1-43856 


1-42612 


1-40896 


38733 


1-36157 


1-33209 


1-29939 


1-26404 


84 


1-46608 


1-46349 


1-45575 


1-44299 


1-42537 


40317 


1-37672 


1-34643 


1-31282 


1-27646 


85 


1-48353 


1-48087 


1-47294 


1-45985 


1-44178 


1-41900 


1-39186 


1-36076 


1-32623 


1-28886 


86 


1-50098 


1-49826 


1-49013 


1-47671 


1-45819 


43483 


1-40699 


1-37508 


1-3&63 


1-30124 


87 


1-51844 


1-51565 


1-50732 


1-49357 


1-47459 


1-45066 


1-42211 


1-38939 


1-35302 


1-31360 


88 


1-53589 


1-53304 


1-52451 


1-51043 


1-49100 


1-46648 


1-43723 


1-40369 


1-36640 


1-32596 


89 


1-55334 


1-55042 


1-54170 


1-52729 


1-50740 


1-48230 


1-45235 


1-41799 


1-37977 


1-33830 


90 


1-57080 


1-56781 


1-55889 


1*54415 


1-52380 


1'49811 


1-46746 


1-43229 


1-39314 


1-35064 



ft continued. 



75 



= 50 


= 650 


= 60 


= 65 


= 70 


= 75 


= 80 


= 85 


= 00 


* 


75599 


74881 


74195 


73564 


73010 


72554 


72215 


72005 


71934 


46 


77050 


76285 


75553 


74879 


74287 


73800 


73436 


73211 


73135 


47 


78490 


77676 


76896 


76177 


75546 


75025 


74636 


74396 


74314 


48 


79920 


79054 


78225 


77459 


76786 


76230 


75815 


75558 


75471 


49 


81338 


80419 


79538 


78724 


78007 


77414 


76971 


76697 


7U604 


50 


82746 


81772 


80836 


79971 


79208 


78578 


78106 


77814 


-.7715 


51 


84143 


83111 


82120 


81202 


80391 


79720 


79218 


78907 


78801 


52 


85529 


84438 


83388 


82415 


81554 


80842 


80307 


79976 


79864 


53 


8G904 


85752 


84641 


83610 


82698 


81941 


81374 


81021 


80902 


54 


88269 


87052 


85879 


84788 


83822 


83020 


82417 


82042 


81915 


55 


89622 


88340 


87101 


85949 


84926 


84076 


83436 


83039 


82904 


56 


90965 


89614 


88308 


87092 


86011 


85110 


84432 


84010 


838(57 


57 


92297 


90876 


89500 


88217 


87075 


86122 


85404 


84957 


84805 


58 


93619 


92125 


90677 


89:525 


88119 


87112 


86352 


85878 


85717 


59 


94930 


93362 


91839 


90415 


89144 


88080 


87276 


86773 


86603 


60 


96231 


9458G 


92986 


91488 


90148 


89025 


88175 


87643 


874G2 


61 


97521 


05797 


94118 


92543 


91132 


89948 


89049 


88486 


88 k 295 


62 


98802 


96996 


95236 


93581 


92096 


90848 


89898 


89303 


89101 


63 


1-00072 


98183 


96339 


94602 


93041 


91725 


90723 


90094 


89871) 


64 


1-01333 


91)358 


97427 


-95606 


93965 


92580 


91523 


90858 


90631 


65 


1-02585 


1 '00522 


98502 


96593 


94870 


93412 


92297 


91595 


91355 


66 


1-03827 


1-01674 


99562 


97564 


95756 


94222 


9:5047 


92305 


92050 


67 


1-05060 


1-02815 


1-00609 


1)8518 


96G22 


95010 


93771 


92987 


92718 


68 


1-06284 


1 03945 


1-01643 


99456 


97469 


95775 


94470 


93642 


9:5358 


69 


1-07500 


1-05064 


1-02664 


1-00379 


98298 


96519 


95144 


94270 


93969 


70 


1-08707 


1-06173 


1-03672 


1-01286 


99108 


97240 


95793 


94870 


91552 


71 


1-09907 


1-07272 


1-04668 


1-02178 


99900 


97940 


90417 


95442 


9510G 


72 


1-11098 


1-08362 


1-05651 


1-03056 


1-00674 


98619 


97016 


95987 


95G30 


73 


12283 


1-09442 


1-06624 


1-03919 


1-01431 


99278 


97590 


96503 


9G12G 


74 


13460 


1-10513 


1-07586 


1-04709 


1-02172 


99916 


98141 


96992 


9G593 


75 


14631 


1-11577 


1-08537 


1-05607 


1-02896 


1-00534 


98667 


97453 


97030 


76 


15795 


1-126,'{2 


1-09478 


1-06432 


1-03605 


1-01133 


99170 


97887 


97437 


77 


16954 


1-13680 


1-10410 


1-07245 


1-04300 


1-01714 


99650 


98293 


97815 


78 


18107 


1-14721 


1-11333 


1-08047 


1-04981 


1-02277 


1-00107 


98671 


981G3 


79 


19255 


1-15755 


1-12249 


1-08839 


1-05648 


1-02823 


1-00543 


99023 


98481 


80 


1-20399 


1-16784 


1-13156 


1-09621 


1-06304 


1-03354 


1-00958 


99318 


98769 


81 


1-21538 


1-17807 


1-14057 


1-10395 


1-06948 


1-03870 


1-01354 


99646 


99027 


82 


1-22673 


1-18825 


1-14952 


1-11161 


1-07582 


1-04372 


1-01731 


99920 


99255 


83 


1-23805 


1-19839 


1-15841 


1-11920 


1-08207 


1-04863 


1-02091 


1-00168 


99452 


84 


1-24934 


1-20850 


1-16726 


1-12673 


1-08825 


1-05343 


1-02436 


1-00394 


99619 


85 


1-26061 


l-2i857 


1-17606 


13421 


1-09135 


1-05813 


1-02768 


1-00598 


99756 


86 


1-27186 


1-22862 


1-18484 


14165 


1-10041 


1-06277 


1-03089 


1-00784 


99863 


87 


1-28310 


1-23865 


1-19359 


1490G 


1-10642 


1-06735 


1-03401 


1-00954 


99939 


88 


1-29432 


1-24867 


1-20233 


15645 


1-11241 


1-07188 


1-03708 


1-01113 


99985 


89 


1-30554 


1-25868 


1-21106 


16383 


1-11838 


1-07641 


1-04011 


1-01266 


1-00000 


90 



7 6 



XXVI. COMPLETE ELLIPTIC FUNCTIONS. 



e 


F, . 


E, 





F, 


E, 


e 


Fi 


Ei 


GO 


1-57080 


1-57080 


30 


1-68575 


1-46746 


60 


2-15652 


1-21106 


1 


1-57092 


1-57068 


31 


69411 


1-46077 


61 


2-18421 


1-20154 


2 


1-57127 


1-57032 


32 


70284 


1-45391 


62 


2-21319 


1-19205 


3 


1-57187 


1-56972 


33 


71192 


1-44687 


63 


2-24355 


1-18259 


4 


1-57271 


1-56888 


34 


72139 


1-43966 


64 


2-27538 


1-17318 


6 


1-57379 


1-56781 


35 


73125 


1-43229 


65 


2-30879 


1-16383 


6 


1-67511 


1-56650 


36 


74150 


1-42476 


66 


2-34390 


1-15455 


7 


1-57668 


1-56495 


37 


1-75217 


1-41707 


67 


2-38087 


1-14535 


8 


1-67849 


1-56316 


38 


1-76326 


1-40924 


68 


2-41984 


1-13624 





1-58054 


1-56114 


39 


1-77479 


1-40126 


69 


2-46100 


1-12726 


10 


1-58284 


1-55889 


40 


1 -78(577 


1-39314 


70 


2-50455 


1-11838 


11 


1-58539 


1-55640 


41 


1-79922 


1-38189 


71 


2-55073 


1-10964 


12 


1-68820 


1-55368 


42 


1-81216 


1-37650 


72 


2-.V.W82 


1-10106 


13 


1-59125 


1-55073 


43 


1-82560 


1-36800 


73 


2-65214 


1-09265 


14 


1-69457 


1-54755 


44 


1-83957 


1-35938 


74 


2-70807 


1-08443 


15 


1-59814 


1-54415 


45 


1-85407 


1-35064 


75 


2-76806 


1-07641 


10 


1-60198 


1-51052 


46 


1-86915 


1-34181 


76 


2-8.5267 


1-06861 


17 


1 -60008 


1-53667 


47 


1-88481 


1-33287 


77 


2-90256 


1-06106 


18 


1-61045 


1-532(50 


48 


1-90108 


1-32384 


78 


2-97857 


1-05378 


19 


1-61610 


1-52831 


49 


1-91800 


1-31473 


79 


3-06173 


1-04679 


20 


1-62003 


1-52380 


50 


1-93558 


1-30554 


80 


3-15339 


1-04011 


21 


1-62523 


1-51908 


51 


1-95386 


1-29628 


81 


3-25530 


1-03379 


22 


1-63073 


1-51415 


52 


1-97288 


1-28695 


82 


3-36987 


1-02784 


23 


1-63652 


1-50901 


53 


1-99267 


1-27757 


83 


3-50042 


1-02231 


24 


1-64260 


1-50366 


64 


2-01327 


1-26815 


84 


3-651,86 


1-01724 


25 


1-64900 


1-49811 


55 


2-03472 


1-25868 


85 


3-83174 


1-01266 


26 


1-65670 


1-49237 


56 


2-05706 


1-24918 


86 


4-05276 


1-00865 


27 


1-6G272 


1-48643 


57 


2-08036 


1-23966 


87 


4-33865 


1-00526 


28 


1-67006 


1-48029 


58 


2-10466 


1-23013 


88 


4-74271 


1-00258 


29 


1-67773 


1-47397 


59 


2-13002 


1-22059 


89 


5-43491 


1-00075 














90 


Inf. 


1-00000 



77 



xxvii Loo r(/). 



X 





1 


2 


3 


4 


5 


6 


7 


8 





ro 


T-9( ) 


9753 


9513 


9280 


9053 


8834 


8621 


8415 


8215 


8021 


1-1 


I- 978:34 


7653 


7478 


7310 


7147 


6990 


6839 


6694 


6551 


6121 


1-2 


T-96292 


6169 


6052 


5910 


5833 


5732 


5636 


5545 


6459 


5378 


1-3 


1 '95302 


5231 


5165 


5104 


5047 


4995 


4948 


4905 


4868 


4834 


T4 


1-94805 


4781 


4761 


4745 


4734 


4726 


4724 


4725 


4731 


4741 


1-5 


1-94754 


4772 


4791 


4820 


4850 


4884 


4921 


4963 


5008 


5057 


re 


1-95110 


5167 


5227 


5'29 1 


5359 


5430 


5505 


5583 


5665 


5700 


1'7 


1-95839 


6931 


6027 


6126 


6229 


6335 


6444 


6556 


6672 


6791 


1-8 


1-96913 


7038 


7167 


7298 


7433 


7571 


7712 


7856 


8004 


8154 


T9 


1-98307 


8463 


8622 


8784 


89-10 


9117 


9288 


9162 


9(138 


9818 



XXVIII. Loo I (x \ i). 



X 


Lou i (x + 1) 


x 


Lou r(.c+ 1) 


x 


Lou i'U + 1) 


.r 


Loo I(JH 1) 


I 


-00000 


26 


26*60502 


51 


66-190(55 


76 


111-27513 


2 


30103 


27 


28'0,'i698 


52 


67-90665 


77 


11 3- 16! 92 


3 


77815 


28 


29-4X414 


53 


69-03092 


78 


115-05401 


4 


1-38021 


29 


30-94654 


54 


71-36332 


79 


116-95164 


5 


2-07918 


30 


32-42366 


55 


73-10368 


80 


118-85473 


6 


2-85733 


31 


33-91502 


56 


74-85187 


81 


120-76321 


7 


3-70213 


32 


35-42017 


57 


76-60774 


82 


122-67703 


8 


4-60552 


33 


36 -93809 


58 


78-37117 


83 


124-59610 


9 


5-55976 


34 


38' 17016 


59 


80-14202 


84 


126-52038 


10 


6*55976 


35 


40-01423 


60 


81-92017 


85 


128-44980 


11 


7-60116 


36 


41-57054 


61 


83-70550 


86 


130-38430 


12 


8-68034 


37 


43-13874 


62 


85-49790 


87 


132-32382 


13 


9-79128 


38 


44-71852 


63 


87-29721 


88 


134-26830 


14 


10-94041 


39 


46-30959 


64 


89-10842 


89 


136-21769 


15 


12-11650 


40 


47-91165 


65 


90-91 633 


90 


138-17194 


16 


13-32002 


41 


49-52443 


66 


92-735*7 


91 


140-13098 


17 


14-55107 


42 


51-14768 


67 


94-56195 


92 


142-09477 


18 


15-80634 


43 


52-78115 


68 


96-39446 


93 


144-06325 


19 


17-08509 


44 


54-42460 


69 


98-23331 


94 


146-03638 


20 


18-38612 


45 


56-07781 


70 


100-07841 


95 


148-01410 


21 


19-70834 


46 


57-74057 


71 


101-02966 


96 


149-09637 


22 


21-05077 


47 


59-41267 


72 


103-78700 


97 


151-98314 


23 


22-41249 


48 


61-09391 


73 


105-06032 


98 


153-97437 


24 


23-79271 


49 


62-78410 


74 


107-51956 


99 


155-97000 


25 


25-19065 


50 


64-48307 


75 


109-39461 


100 


157-97000 



XXIX. ZONAL SURFACE HARMONICS. 



X 


PiGO 


P(*) 


Pa(*) 


P(*) 


P.(*) 


P.() ' 


Pi() 


00 


+00 


-50000 


-00000 


+'37500 


+00000 


-31250 


+'00000 


01 


+01 


-49985 


-01500 


+37463 


+01874 


-31184 


-02186 


02 


+02 


-49940 


- -02998 


+37350 


+03743 


-30988 


- -04359 


03 


+03 


- -49865 


-04493 


+37163 


+05601 


-30661 


- -06509 


04 


+04 


-49760 


-05984 


+36901 


+07444 


- -30205 


- '08624 


05 


+05 


-49625 


-07469 


+36565 


+09266 


-29622 


- 10693 


06 


+ 00 


- '49460 


-08946 


+36156 


+11062 


-28913 


- -12703 


07 


+07 


- -49205 


-10414 


+35673 


+12826 


-28081 


- -14644 


08 


+08 


- -49040 


-11872 


+35118 


+14555 


-27130 


- 16506 


09 


+09 


-48785 


-13318 


+34491 


+16242 


- -26063 


- 18278 


10 


+10 


-48500 


-14750 


+33794 


+17883 


- -24883 


-19949 


11 


+11 


-481X5 


-16167 


+ -33027 


+19473 


- -23595 


-21511 


12 


+12 


- -47840 


- -17568 


+ 32191 


+21008 


-22204 


-22955 


13 


+13 


-47465 


-18051 


+ 31287 


+22482 


-20715 


-24271 


14 


+14 


-47060 


-203 14 


+30318 


+23891 


-19133 


-25453 


15 


+15 


- '46025 


-2 1056 


+29284 


+25232 


-17465 


-26492 


16 


+16 


-46160 


-22976 


+ '28187 


+26499 


-15716 


-27383 


17 


+17 


- '45665 


-21272 


+27028 


+27688 


-13894 


-28119 


18 


+18 


-45140 


-25542 


+25809 


+28796 


-12005 


-28695 


19 


+19 


-44585 


- -20785 


+24533 


+29818 


-10057 


-29107 


20 


+20 


-44000 


-28000 


+23200 


+30752 


-08058 


-29352 


21 


+21 


- -43385 


-29185 


+21813 


+31593 


-00014 


-29426 


22 


+22 


- -42740 


- -30338 


+20375 


+32339 


- -03936 


-29327 


23 


+23 


- -42065 


-31458 


+18887 


+32986 


-01830 


-29055 


24 


+24 


-41360 


-32544 


+17352 


+33531 


+00294 


-28610 


25 


+25 


- -40625 


-33594 


+15771 


+33972 


+02428 


-27992 


26 


+20 


- -39860 


- -34606 


+14149 


+34307 


+01562 


-27203 


27 


+27 


- -39065 


- -35579 


+12488 


+34532 


+06687 


-26246 


28 


+28 


- -382-10 


-36512 


+10789 


+34647 


+08795 


-25124 


29 


+29 


-37385 


-37403 


+09057 


+34650 


+'10875 


-23843 


30 


+30 


- -36500 


- -38250 


+07294 


+34539 


+12918 


-22407 


31 


+31 


- '35585 


- -39052 


+05503 


+34312 


+14915 


-20824 


32 


+32 


- -34640 


- -39808 


+03688 


+ 33970 


+16856 


-19100 


33 


+33 


- -33605 


-40516 


+01851 


+ 33512 


+18732 


-17244 


34 


+34 


- -321*60 


-41174 


- -00004 


+32937 


+20534 


-15266 


35 


+35 


-31625 


-41781 


- -01872 


+32245 


+22251 


-13176 


36 


+36 


-30500 


-42336 


- -03752 


+31438 


+23875 


-10984 


37 


+37 


-29105 


- '42837 


- -05638 


+30514 


+25397 


-08704 


38 


+38 


-28340 


- -43282 


- -07528 


+29477 


+26808 


-06347 


39 


+39 


-27185 


- -43670 


-09416 


+28326 


+28100 


-03927 


40 


+40 


- -26000 


- -44000 


-11300 


+27064 


+29264 


-01459 


41 


-r-41 


-24785 


-4 4270 


-13175 


+25693 


+30291 


+01042 


42 


+42 


-23540 


-44 178 


-15036 


+24215 


+31176 


+03561 


43 


+43 


-22265 


- -44623 


-16880 


+22633 


+31909 


+06082 


44 


+44 


-20960 


- -44704 


-18702 


+20951 


+32486 


+08587 


45 


+45 


-19625 


-44719 


-20497 


+19172 


+32898 


+11060 


46 


+46 


-18260 


-44666 


-22261 


+17301 


+33141 


+13483 


47 


+47 


-16865 


- -44544 


-23989 


+15341 


+33209 


+15838 


48 


+48 


-15440 


-44352 


-25676 


+13298 


+33098 


+18107 


49 


+49 


-13985 


-44088 


-27316 


+11177 


+32804 


+20272 


60 


+50 


-12500 


-43760 


-28906 


+08984 


+32324 


+22314 



79 



ZONAL SURFACE 






PiM 


PM 


Pi(*) 


PW 


PiW 


P.(*) 


Pf() 


51 


+51 


-10985 


-43337 


-30440 


+06726 


+81665 


+24217 


52 


+'52 


-09440 


-42848 


-31912 


+04409 


+30796 


+25961 


53 


+53 


-07865 


-42281 


-33317 


+02041 


+29747 


+27530 


54 


+54 


-06260 


-41634 


-34649 


-00372 


+28506 


+28906 


55 


+56 


' '04625 


-40906 


-35904 


-02819 


+27077 


+30074 


56 


+56 


-02960 


-40096 


-37074 


-05294 


+25460 


+31016 


57 


+57 


-01265 


-39202 


- -38155 


-07786 


+23660 


+31719 


58 


+58 


+00460 


- -38222 


-39140 


-10285 


+-216S1 


+32169 


59 


+59 


+02215 


-37155 


- '40024 


-12781 


+19528 


+32353 


60 


+-GO 


+04000 


-36000 


-40800 


-15264 


+17210 


+32260 


61 


+61 


+05815 


-34755 


-41462 


-17721 


+14733 


+31880 


62 


+62 


+07660 


-33118 


-42004 


-20142 


+12109 


+31207 


63 


+63 


+09535 


-31988 


-42418 


-'22512 


+09348 


+30232 


64 


+64 


+11440 


-30164 


-42700 


-24819 


+00402 


+28954 


65 


+65 


+13375 


-28844 


-42841 


-27019 


+03467 


+27371 


66 


+66 


+15340 


-27126 


-42836 


-29188 


+00379 


+25483 


67 


+67 


+17335 


-25309 


-42076 


-'31220 


-02785 


+23295 


68 


+68 


+19300 


-23392 


-42356 


-'33131 


-00006 


+20813 


69 


+ 69 


+21415 


-21373 


-41809 


-34903 


-09201 


+18049 


70 


+70 


+23500 


-19250 


-41206 


- -30520 


-12529 


+15016 


71 


+'7i 


+ 25615 


-17022 


-40361 


-37964 


-15782 


+11731 


72 


+72 


+ 27760 


-14088 


-39327 


-39217 


-18901 


+08217 


73 


+'73 


+29935 


-12246 


-38095 


-4021,0 


- -22130 


+04499 


74 


+74 


+ 32140 


- -09694 


-30059 


-4 1074 


-25175 


+00609 


'75 


+75 


+ 34375 


-07031 


- '35010 


-41638 


-28078 


-03418 


76 


+76 


+36640 


-04256 


-33140 


-41931 


-30807 


-07541 


77 


+77 


+38935 


-01307 


-31043 


-41932 


-33325 


-11713 


78 


+78 


+41260 


+01638 


-28709 


-41018 


-3f>r>H9 


-15881 


79 


+79 


+ 43615 


+04760 


-26131 


-4()%G 


-37557 


-19987 


80 


+80 


+46000 


+'08000 


-23300 


-39952 


-39180 


-23965 


81 


+81 


+48415 


+ 11360 


-20208 


-38552 


-40409 


-27743 


82 


+82 


+50860 


+ 14842 


-10847 


- -36739 


-41193 


-31240 


83 


+83 


+ 53335 


+ 18447 


-13207 


-34489 


-4 1475 


-34368 


84 


+84 


+55840 


+22176 


-09281 


-31774 


-41198 


-37033 


85 


+85 


+ 58375 


+26031 


- -050t>0 


- -28506 


-10300 


-39130 


86 


+86 


+60940 


+30014 


-00534 


-24838 


-38716 


-40545 


87 


+87 


+ 63535 


+34126 


+01305 


-20559 


-30379 


-41150 


88 


+88 


+ 66160 


+38308 


+09467 


-15099 


-33217 


-40829 


*89 


+'89 


+68815 


+42742 


+14960 


-10228 


-29156 


-39423 


90 


+90 


+'71500 


+47250 


+20794 


-04114 


-24116 


-36782 


91 


+91 


+74215 


+51893 


+'26978 


+02076 


-18018 


- -32743 


92 


+92 


+70960 


+56672 


+33522 


+10175 


-10774 


-27121) 


93 


+93 


+'79735 


+'61589 


+'40435 


+18417 


-02295 


-19749 


94 


+94 


+ 82540 


+66646 


+47728 


+27438 


+07512 


-10404 


'95 


+95 


+85375 


+71844 


+55409 


+37274 


+18745 


+01123 


96 


f 96 


+88240 


+77184 


+63489 


+47962 


+31506 


+15000 


97 


+97 


+91135 


+82668 


+71978 


+59539 


+45899 


+31650 


'98 


+98 


+94060 


+88298 


+80886 


+72045 


+62035 


+51151 


99 


+99 


+97015 


+94075 


+90223 


+85518 


+80029 


+73838 


TOO 


+1-00 


+1-00000 


+1-00000 


+1-00000 


+1-00000 


+1-00000 


+ 1 '00000 



















So 



XXX. BESSEL FUNCTIONS. 



X 


Jt(*) 


JiW 


X 


JoCO 


JiC*) 


X 


Jt(*) 


Ji(*> 


O'O 


+ 1-00000 


+00000 


5-0 


-17760 


-32758 


10-0 


-24594 


+04347 


O'l 


-f- -99750 


+04994 


5*1 


-14433 


-33710 


10-1 


-24903 


+01840 


0*2 


+99002 


+09950 


6'2 


-11029 


-34322 


10'2 


-24962 


-00662 


0'3 


+977(53 


+14832 


5'3 


-07580 


-34596 


10-3 


-'24772 


-03132 


0'4 


+96040 


+19603 


5'4 


-04 121 


-34534 


10-4 


-24337 


-05547 


0-6 


+93847 


+24227 


5*5 


-00684 


-34144 


10'5 


-23665 


-07885 


0-6 


+91200 


+28670 


5'6 


+02697 


-33433 


10'6 


-22764 


-10123 


0'7 


+-H8120 


+32900 


6'7 


+'05992 


-32415 


10-7 


-21644 


-12240 


0'8 


+84629 


+30884 


5'8 


+ 09170 


-31103 


10-8 


-20320 


-14217 


0-9 


+80752 


+40595 


5'9 


+11203 


-29514 


10'9 


- 18806 


-16035 


ro 


+76520 


+4400.) 


6-0 


+15065 


-27668 


11-0 


-17119 


-17679 


I'l 


+71902 


+47000 


6-1 


+ 17729 


-25586 


ll'l 


-15277 


-19133 


ra 


+67113 


+49829 


6'2 


+ 20175 


-23292 


11*2 


-13299 


- -20385 


T3 


+ 62009 


+52202 


6'3 


+ 22381 


-20809 


11-3 


-11207 


-.21426 


T4 


+ 56686 


+51195 


6'4 


+ 24331 


-18164 


11-4 


-09021 


-22245 


1-5 


+51183 


+55794 


6'5 


+ 26009 


- 15384 


11-5 


-06765 


-22838 


1-6 


+455-10 


+56990 


6'6 


+ 27404 


-12498 


11-6 


-04462 


-23200 


1-7 


+39798 


+57777 


6'7 


+28506 


- -09534 


11-7 


-02133 


-23330 


1-8 


+331)1)9 


+58152 


6'8 


+ '29310 


-06522 


11 '8 


+ 00197 


-23228 


1-9 


+28182 


+ 58116 


6'9 


+ 29810 


-03490 


11-9 


+02505 


-22898 


2'0 


+22389 


+57672 


7'0 


+ 30008 


-00168 


12-0 


+04769 


-22345 


2-1 


+16661 


+ 56829 


7-1 


+ 29905 


+02515 


12-1 


+ 06967 


-21575 


2'2 


+'11036 


+ 55596 


7'2 


+ 29507 


+05433 


12'2 


+09077 


-20598 


2'3 


+05554 


+ 53987 


7'3 


+ 28822 


+08257 


12'3 


+11080 


-19426 


2'4 


+00251 


+52019 


7'4 


+ 27860 


+10963 


12'4 


+12956 


-18071 


2'5 


-04838 


+ 4 9709 


7'5 


+ 26634 


+13525 


12-5 


+14688 


-16548 


2'6 


-09680 


+ 47082 


7'6 


+ 25160 


+15921 


12-6 


+16261 


-14874 


2'7 


-14245 


+ 44160 


7'7 


+ 23456 


+18131 


12'7 


+17659 


-13066 


2'8 


-18504 


+ 40971 


7'8 


+ 21541 


+20136 


12'8 


+18870 


-11143 


2'9 


-22431 


+37513 


7'9 


+ 19436 


+21918 


12'9 


+19884 


-09125 


3'0 


-26005 


+33906 


8'0 


+17165 


+ 23464 


13-0 


+20693 


-07032 


3'1 


-29206 


+ -30002 


8-1 


+14752 


+24761 


13-1 


+21289 


-04885 


3*2 


-32019 


+ 26134 


8'2 


+ 12222 


+25800 


13-2 


+21669 


-02707 


3'3 


-34430 


+ 22066 


8'3 


+ 09601 


+26,074 


13'3 


+21830 


-00518 


3'4 


-36430 


+17923 


8'4 


+ 06916 


+27079 


13'4 


+21773 


+ 01660 


3*5 


-38013 


+13738 


8'5 


+04194 


+27312 


13'5 


+21499 


+03805 


3'6 


-39177 


+09547 


8-6 


+ 01462 


+27275 


13'6 


+21013 


+05896 


3'7 


-39923 


+ 05383 


8'7 


-01252 


+26972 


13'7 


+20322 


+07914 


3'8 


-40256 


+ 01282 


8'8 


03923 


+26407 


13-8 


+19434 


+09839 


3'9 


-40183 


-02724 


8'9 


-06525 


+25590 


13'9 


+18358 


+11652 


4'0 


-39715 


-06604 


9'0 


-09033 


+24531 


14*0 


+17107 


+ 13338 


4'1 


- -38867 


-10327 


9*1 


-11424 


+23243 


14'1 


+15695 


+14878 


4*2 


- -37656 


-13865 


9*2 


-13675 


+21741 


14'2 


+14137 


+16261 


4'3 


-36101 


-17190 


9'3 


-15766 


+20041 


14'3 


+12449 


+17473 


4'4 


-34226 


-20278 


9'4 


-17677 


+18163 


14-4 


+10648 


+18503 


4*5 


-'32054 


-23106 


9'5 


-19393 


+16126 


14'5 


+08754 


+19343 


46 


-29614 


-25655 


9-6 


-20898 


+13952 


14'6 


+06786 


+19985 


4'7 


-26!)33 


-27908 


9'7 


-22180 


+ 11664 


14'7 


+04764 


+20425 


4*8 


- -24043 


-298r>0 


9'8 


-23228 


+ 09284 


14-8 


+02708 


+ 20660 


4-9 


-20974 


-31169 


9*9 


- -24034 


+ 06837 


14'9 


+00639 


+20688 


6-0 


- 17760 


-32758 


10-0 


-24594 


+04347 


15-0 


-01422 


+ 20510 



c> 

I 



o 

125 



t 



fc$;S 
isites 



IM i 







i$ 



+ + ++++4- 4-4-+++ 



O t <O 

OOO D 

^(^0 o 

*l "l "l + 



> -i o b~ o * t~- 

O C4 tO CN O 
O O O I-H O* 



o>co oooo I 



s^s^s a 
*i "i 1 *i + + 



O O O O O O CM O CN i-H Ol O 
O O O O O O O O ~t JN <Nep( 

" " " 



r- 

CO O 

^ o 



CO O O -<f 
iO 00 I- l^ 



i i i 



'Ot^-O'Ol^ 

-- 



O THiOC^I 

o o o 1^1 o 



+++! 



OOC^'tfCO'^ 

COb-CO'O'M 

tO>OCiCi 

T"? T 1 T 1 9* 

M HHHh 



3 O I kO 00 

5 O r-< lO T-4 

O <N "O 
. _ 00 -H 



D OJ 00 OS <O -t OO O b 



. 
ClCO'M'M f-iTHl'.rrk 



4HM l l 



O r-t UO O OO C^ 

co oo oo io -< o5 

O -H t O I H 

++++"l "l 



- 
i" o t >-*t>.i>.a>t>. 



+4-+l-4- l l l l 4- 



8SS35 
4-4-Vl "l *l 



SIQT^COO -^ o> o h -^ <c>o>t--e^oo 

o-^co tD^o-^boo cocot^coiN 

OO^ C^ CO CO i I O C^C^O-HC^ 

4-++4- +4-4-4- "l "l "l *l ++ 



l + + 



O O CO CO CO rj< O *G t> O "* O 00 ^ 
OOrH C^OOOCO*^ 1 tOO^OC^C^i 
-TC^i-t r-il-t-^'O'O OSOfiMOS1O 



QO ^ -^ -^ O t 
rH tO I O O CD 
OSC^OCiO O 



O iO C?l O OOt-'O ig 



(NOi O 

>COf Oi 



O * t C 



+ + + + ++! 



! l l +++ 



4 ' i CS *! *t'OT't>C s < T^COQOt"-^ O 

i O "- -^ i^COQO'-tuO -^ 00 O Q D 

-CO-<TH C^i-tOC^rH Oi-Or-< TH 

" * " " * ' ' 



Tf O CO O CO O CO 5Ol--l'.iO 

CO-^" ^t^C^I-CO OOiOSOOO 

XNM pr-ic^o^H < ^ l< r >o 7*'r ( 
" " " * ' " 



+++ I l l ++ 



l "l 4- ++! 'l "l + 



oosoio oooo*oco t*a>o>cor^ ooooco <N 

0*000^ tOOO^OCO OJ-H?OOSO C^CiQOCO^D O 

^cooi> t^oo~<o o t^ to -^ ^TOCOO t-- 

^O^^O* t*OOt>.O> '*1'l>^'Ot s -Ht>O-'J* O 

++'l "l 'l 4-++1 *l "l +++ "l 'l Vl + + 



rHiHiHrHrH 



>25 1 





388 



8S 



> o o <: 



O O *-" <N CO to 



^ _ - 

OOO OOOOO O rH <?> CO LO t^- 
O O O OOOOO OOOOO O 



I 



?88 



-^?l tO 5 



"<* t" rH OO t- -( 00 t- <M tO 

- O O r- 1 rH ^J H^!O30C'1OO "O 

50 OOOOO O O O rH rH <M 



o o o 
O 00 



>S.:2 g^2^- ^^^ot 

OSOO ^ oooo^ 
OOOOO 



w 



PQ 

I 



.-CyiC-l^^ COI>.tOC5C?> rHtOrHCi-^ C^rH<MQ 

5J <0 >0 O to OOCOril-tO C^CMtOOOO ?-l>.^C 



hOO COr^OOt>-QO -H> 
COO t>-CO*efCOO l^ t 



>t*ooo r>-tocicio> -^cot>cooo ^ioor-ito coo^voco TH 

SSt^ZJ"^ <MC5Trcjco (Mt^r-oio orfi-ntoco co-^Cicoo co 

^^^OrH <Ncotocv^ rJSP.os:S9 ^999 co(N<Ntp<^ ^ 

THrHC^C^ COi^OtOCIO rH 



5<Ml>t>O iCOOt-M* 

?O(Mcoco i>.'-cioaip 

5OOOO -rH(>J<MCO*b 



?Zi2r% cSSS^S J 






SO CO O <O 00 C5 OO CN tp^rH^.H ^ CO rH t* -^ vo to to CO CO tO 

>OOt- OO rHtOOTfit^. O^OOlOrH CO'^'OOIO OSOftOiO CO 

oo'rco<N *o^tooo*H cirHgsioo oeor>-C5Tt* iftt>.ooo<M co 

S5S^2 55^959^ 4701^ t-co a>t^<pt^rH ^-^^^^ ^, 



co co -^ o to oo 



" rH -Tf O O 
rH HrH (M 



-O> <N<MOCO-1 O 

4D O"t"rHCsOS rf" 

JrH CO^OOt^. CM 



OOOOO 



OW^fCDOO OtN^QDOO O 



CO CO COCO CO 



XXXIII. ROOTS OF J n ( = 0. 





n = 


n = 1 


n = 2 


n = 3 


n = 4 


n = 5 


1 


2-405 


3-832 


5*135 


6-379 


7-586 


8-780 


2 


5-520 


7-016 


8-417 


9-760 


11-064 


12*339 


3 


8-654 


10-173 


11-620 


13-017 


14-373 


15-700 


4 


11-792 


13-323 


14*796 


16*224 


17-616 


18-982 


5 


14-931 


16-470 


17'960 


19*410 


20-827 


22-220 


6 


18-071 


19-616 


21*117 


22-583 


21-018 


25-431 


7 


21-212 


22-760 


24-270 


25-749 


27-200 


28-628 


8 


24-353 


25-903 


27-421 


28-909 


30-371 


31-813 


9 


27-494 


29-047 


30-571 


32-050 


33-512 


34-983 



ROOTS OF J (V) = 0, AND 



= 0. 





- FOR J (^ v ) = 


- roil .1 )(.*') = 




L i<ou J (.0 = 


- FOR Ji() = 


1 


0-7655 


1*2179 


7 


6-7519 


7*2448 


2 


1-7571 


2*2330 


8 


7-7516 


8*2454 


3 


2-7546 


3-2383 


9 


8-7514 


9*2459 


4 


3-7534 


4*2411 


10 


9-7513 


10-2463 


5 


4-7527 


5*2428 


11 


10*7512 


11-2466 


6 


5-7522 


6*2439 


12 


11-7511 


12-2469 



1 

3 
5 

7 
9 

11 
-1 
-3 

-5 

-7 

-9 

-11 



XXXIV.-.T i+i (r). 



em x 

sin x 

- x cos x 

/3 __\ ina; _3 
/15^6\ . /1,5 \ 

f 10 ^ _ 1? i i\ _ (I 05 _ i Qx \ 
/045 420 15\ . /945 1 

COS X 

COS X 

Bin 



/15_6' 
<105 45 



/15 



420 , 



XXXV.I = -?- I e-di 



X 


I 


X 


I 


X 


I 


X 


I 


X 


I 


X 


I 


01 


01128 


51 


52924 


1-01 


84681 


1'51 


96728 


2-01 


99552 


2'51 


99961 


02 


02256 


52 


53790 


1'02 


85084 


1-52 


96841 


2-02 


99572 


2*52 


99963 


03 


03384 


53 


54646 


1'03 


85478 


1-63 


96952 


2-03 


99591 


2'53 


99965 


04 


04511 


54 


55494 


ro4 


85865 


1-54 


97059 


2'04 


99609 


2'54 


99967 


05 


05637 


55 


66332 


1'05 


86244 


1-55 


97162 


2-05 


99626 


2*55 


99969 


'06 


06762 


56 


57162 


1-06 


86614 


1'56 


97263 


2-06 


99642 


2'56 


99971 


07 


07886 


57 


57982 


1'07 


86977 


1'57 


97360 


2-07 


99658 


2'57 


99972 


08 


09008 


58 


68792 


1-08 


87333 


1'58 


97455 


2-08 


99673 


2'58 


99974 


09 


10128 


'59 


59594 


1'09 


87680 


1'59 


97546 


2'09 


99688 


2*59 


99975 


10 


11246 


60 


60386 


no 


88021 


1'60 


97635 


2'10 


99702 


2*60 


99976 


11 


12362 


61 


61168 


I'll 


88353 


rei 


97721 


211 


99715 


2'61 


99978 


12 


13476 


62 


61941 


ri2 


88671) 


1-62 


97804 


212 


99728 


2'62 


99979 


13 


14587 


63 


62705 


ri3 


88907 


1*63 


97884 


213 


99741 


2'63 


99980 


14 


15695 


64 


63459 


ri4 


89.108 


1-64 


979(52 


214 


99753 


2'64 


99981 


15 


1G800 


65 


64203 


115 


896 12 


T65 


98038 


215 


99764 


2'65 


99982 


16 


17901 


'66 


64938 


1-16 


89910 


T66 


98110 


216 


99775 


2'66 


99983 


17 


18909 


67 


65663 


1'17 


90200 


1'67 


98181 


217 


99785 


2'67 


99984 


18 


20093 


'68 


66:578 


1-18 


90484 


T68 


98249 


218 


9979:. 


2'68 


99985 


19 


211H4 


'69 


67084 


1-19 


907(51 


1-69 


98315 


219 


99805 


2*69 


99986 


20 


22270 


70 


67780 


1-20 


91031 


1'70 


98379 


2-20 


99814 


2*70 


99987 


21 


23352 


*71 


68467 


1-21 


91296 


1-71 


98141 


2'21 


99822 


2'71 


99987 


'22 


24430 


72 


69143 


T22 


91553 


T72 


98500 


222 


90831 


2'72 


99988 


*23 


25502 


73 


69810 


1-23 


91805 


1-73 


98558 


2'23 


99839 


2'73 


99989 


24 


26670 


74 


70468 


1-24 


92051 


T74 


98(513 


2'24 


90816 


2*74 


99989 


25 


27633 


75 


71116 


1-25 


92290 


T75 


98G67 


2-25 


99854 


2*75 


99990 


*26 


28690 


76 


71754 


1-26 


92524 


1-76 


98719 


2'26 


99861 


2'76 


99991 


27 


29742 


77 


72382 


1-27 


92751 


1'77 


98769 


2'27 


99867 


2-77 


99991 


28 


30788 


78 


73001 


1-28 


92973 


1-78 


98817 


2-28 


99874 


2'78 


99992 


29 


31828 


79 


73610 


1*29 


93190 


1-79 


98864 


2'29 


99880 


2*79 


99992 


30 


32863 


80 


74210 


1-30 


93401 


1'80 


98909 


2'30 


99886 


2*80 


99992 


*31 


33891 


81 


74800 


1-31 


93606 


1'81 


98952 


2*31 


99891 


2'81 


99993 


33 


34913 


'82 


75381 


1'32 


93807 


1-82 


98994 


2'32 


99897 


2'82 


99993 


*33 


35928 


83 


75952 


1-33 


94002 


1'83 


99035 


2-33 


99902 


2'83 


99994 


'34 


36936 


84 


76514 


1-34 


94191 


1-84 


99074 


2'34 


99906 


2'84 


99994 


35 


37938 


85 


77067 


1'35 


94376 


1'85 


99111 


2'35 


99911 


2*85 


99994 


'36 


38933 


86 


77610 


1-36 


94556 


1-86 


99147 


2'36 


99915 


2*86 


99995 


'37 


39921 


87 


78144 


1-37 


94731 


1-87 


99182 


2*37 


99920 


2'87 


99995 


38 


40901 


88 


78669 


1-38 


94902 


1'88 


99216 


2'38 


99924 


2'88 


99995 


39 


41874 


89 


79184 


1-39 


95067 


1-89 


99248 


2-39 


99928 


2*89 


99996 


40 


42839 


90 


79691 


1-40 


95229 


1'90 


99279 


2-40 


99931 


2*90 


99996 


41 


43797 


01 


80188 


1-41 


95385 


1'91 


99309 


2'41 


99935 


2-91 


99996 


42 


44747 


92 


80677 


1-42 


95538 


T92 


99338 


2-42 


99938 


2*92 


99996 


*43 


45689 


93 


81156 


1-43 


95686 


1'93 


99366 


2'43 


99941 


2*93 


99997 


44 


46623 


94 


81627 


1-44 


95830 


1-94 


99392 


2'44 


99944 


2'94 


99997 


45 


47548 


95 


82089 


1-45 


95970 


1*95 


99418 


2*45 


99947 


2*95 


99997 


46 


48466 


96 


82542 


1-46 


96105 


1'96 


99443 


2*46 


99950 


2'96 


99997 


47 


49375 


97 


82987 


1-47 


96237 


1'97 


99466 


2-47 


99952 


2'97 


99997 


48 


50276 


98 


83423 


T48 


96365 


1-98 


99489 


2*48 


99955 


2-98 


99997 


49 


61167 


99 


83851 


1-49 


96490 


1-99 


99511 


2*49 


99957 


2-99 


99998 


50 


52050 


TOO 


84270 


1-50 


96611 


2'00 


99532 


2*50 


99959 


3-00 


99998 






















00 


1-00000 



XXXVI. Ei(a:), 



X 


EiCr) 


i(-*) 


Ci(x) 


8i(x) 


X 


EiCr) 


Ei(-*) 


C1(J) 


BiCr) 


oo 


00 


00 


00 


+ 00000 


50 


+45422 


-5 r >977 


-17778 


+49811 


01 


-4-01793 


-4-03793 


-4-02798 


+01000 


51 


+48703 


-54782 


-16046 


+50269 


02 


-3-31471 


-3-35471 


-3-33491 


+02000 


52 


+51953 


-53622 


-14355 


+51225 


03 


-2-89912 


-2-95912 


-2-92957 


+03000 


53 


+55173 


-52495 


-12707 


+62180 


04 


-2-60126 


-2-68126 


-2-64206 


+04000 


54 


+58365 


61400 


-11099 


+53133 


05 


^2-.%789 


-2-46790 


-2-41914 


+-OJ999 


55 


+6 1529 


-50336 


- -09530 


+54084 


06 


-2-17528 


-2-29531 


-2-23709 


+05999 


56 


+(14668 


-49302 


-07999 


+65033 


07 


-2-01080 


-2-15084 


-2-08327 


+06998 


57 


+67782 


-482% 


- -06504 


+55981 


08 


-1-86688 


-2-02694 


-1-95011 


+07997 


58 


+'70873 


-47317 


- -05044 


+56927 


09 


-1-73866 


-1-91874 


-1-83275 


+08996 


59 


+73941 


-46365 


- -03619 


+'57871 


10 


-1-62281 


-1-82292 


-1-72787 


+09994 


60 


+76988 


-45438 


- -02227 


+ 58813 


11 


-1-51696 


-1-73711 


-1-63308 


+10993 


81 


+80015 


-44535 


--OOH68 


+59763 


12 


-1-41935 


-1-65954 


-1-54665 


+11990 


62 


+83023 


-13656 


+ 004(51 


+60691 


13 


-1-32866 


-1-58890 


-1-46723 


+12988 


63 


+86012 


-42800 


+01768 


+61627 


14 


-1-24384 


-1-52415 


-1-39379 


+13985 


64 


+88984 


-41965 


+03026 


+62661 


15 


-1-16409 


-1-46446 


-1-32552 


+14981 


65 


+91939 


-4 11 52 


+ -04265 


+63494 


16 


-1-08873 


-1-40919 


-1-26176 


+ 15977 


66 


+94878 


- -40359 


+ 05476 


+64424 


17 


-1-01723 


-1-35778 


-1-20196 


+ 1(5973 


67 


+97802 


-39585 


+0(5659 


+65351 


18 


-94915 


-1-30980 


1-14567 


+ 17968 


68 


+ 1-00712 


- 38831 


+07816 


+66277 


19 


-88410 


-1-26486 


-1-09253 


+18962 


69 


+1-03608 


-'38095 


+08946 


+67201 


20 


- -82176 


-1-22265 


-1-04221 


+19956 


70 


+1-06491 


-37377 


+10051 


+68 122 


21 


-76187 


-1-18290 


-99444 


+20949 


71 


+ 1-09361 


-36676 


+11 132 


+69041 


22 


-70420 


-1-14538 


-94899 


+ 21941 


72 


+ 1-12220 


-35992 


+12188 


+69968 


23 


-64853 


-1-10988 


- -90566 


+22933 


73 


+ 1-15068 


-35324 


+13220 


+70873 


24 


- -59470 


-1-07624 


-86427 


+23923 


74 


+1-17906 


-34671 


+14230 


+71786 


25 


-54254 


-1-04428 


-82466 


+24913 


75 


+ 1-20733 


- -34034 


+ 15216 


+72696 


26 


-49193 


-1-01389 


- -78671 


+25903 


76 


+1-23551 


-33412 


+16181 


+73603 


27 


-44274 


-98493 


- 75029 


+26891 


77 


+ 1-2(5360 


-32803 


+17124 


+74608 


28 


-39486 


- 96731 


-71529 


+27878 


78 


+1-20161 


-32209 


+18046 


+76411 


29 


-34820 


- -93092 


- -68161 


+28865 


79 


+ 1-31954 


-31628 


+18947 


+76312 


30 


- -30267 


- -90568 


-64917 


+29850 


80 


+1-34740 


-31060 


+19828 


+77210 


31 


- -25819 


-88151 


-61790 


+ -308:15 


81 


+ 1-37518 


-30504 


+ 20689 


+78105 


32 


- -21468 


-85834 


-68771 


+31819 


82 


+ 1-40290 


-29961 


+21530 


+78998 


33 


-17210 


- 83610 


-55855 


+32801 


83 


+ 1'4305G 


-29430 


+22353 


+79888 


34 


-13036 


- -81475 


- -53036 


+33782 


84 


+1-45816 


-28910 


+23157 


+80776 


35 


-08943 


-79422 


- 50308 


+34763 


85 


+1-48571 


- -28402 


+23942 


+81661 


36 


-04926 


-77446 


-47666 


+35742 


86 


+ 1-51322 


-27905 


+24710 


+82544 


37 


-00979 


-75544 


-45107 


+36720 


87 


+ 1-54067 


- -27418 


+25460 


+83424 


38 


+ '02901 


-73711 


-42625 


+37696 


88 


+1-56809 


- -26941 


+26192 


+84801 


39 


+06718 


- -71944 


-40218 


+38672 


89 


+1-59547 


-26475 


+26908 


+86175 


40 


+10477 


- 70238 


-37881 


+39646 


90 


+1-62281 


-26018 


+27607 


+86047 


41 


+14179 


- -68591 


-35611 


+40619 


91 


+1-66013 


-25671 


+28289 


+86916 


42 


+17828 


-67000 


-33406 


+41591 


92 


+1-67741 


-25134 


+28956 


+87782 


43 


+21427 


-65461 


-31262 


+42561 


93 


+1-70468 


- -24705 


+29606 


+88646 


44 


+24979 


-63973 


-29178 


+43529 


94 


+1-73192 


-24285 


+30242 


+89606 


45 


+28486 


-62533 


-27149 


+44497 


95 


+1-75915 


-23874 


+30861 


+90364 


46 


+31950 


-61 139 


- -25175 


+45463 


96 


+1-78636 


- -23471 


+31466 


+91219 


47 


+35374 


-59788 


-23253 


+46427 


97 


+1-81356 


-23076 


+32056 


+92070 


48 


+38759 


-58478 


-21380 


+47390 


98 


+1-84075 


-22689 


+32632 


+92919 


49 


+42108 


-57209 


-19566 


+48351 


99 


+1-86793 


-22310 


+33193 


+93765 


50 


+45422 


-55977 


-17778 


+49311 


1-00 


+1-89512 


-21938 


+33740 


+94608 



86 



X 


Ei(x) 


Ei(-s) 


Ci(*) 


Si(*) 


X 


Ci(*) 


Si() 


ro 


+1-89512 


-21938 


+33740 


+94608 


20 


+0444 


+1-5482 


1-1 


+2-16738 


- -18599 


+38487 


+1-02869 


25 


-0068 


+1'5315 


ra 


+2-44209 


--15841 


+42046 


+ 1-10805 


30 


-0330 


+1-5668 


ra 


+2-72140 


- 13545 


+44574 


+1-18396 


35 


-0115 


+1-5969 


1-4 


+3-00721 


11622 


+46201 


+ 1-25623 


40 


+ 0190 


+1-5870 


1*6 


+3-30129 


- -10002 


+47036 


+1*32468 


45 


+0186 


+1-5587 


re 


+3-00532 


- -08631 


+47173 


+1-38918 


50 


-0056 


+1-5516 


1-7 


+3-92096 


- -07465 


+46697 


+1*44959 


55 


-0182 


+1-5707 


1-8 


+4-24987 


- -06471 


+ -45681 


+ 1-50582 


60 


-0048 


+1-5867 


1-9 


+4-59371 


- -05620 


+44194 


+1-55778 


65 


+0128 


+1-5775 


2-0 


+4-95423 


- -04890 


+42298 


+1-60541 


70 


+0109 


+1-5616 


2-1 


+5-33324 


-04261 


+40051 


+1-64870 


75 


-0053 


+1-5586 


2*2 


+5-73261 


- -03719 


+ -37507 


+1-68762 


80 


-0124 


+ 1-5723 


2'3 


+6-15438 


- -03250 


+34718 


+1-72221 


85 


--0019 


+ 1-5824 


2'4 


+6-60067 


- -02844 


+31729 


+1-75249 


90 


+0100 


+1-5757 


2'5 


+7-07377 


-02491 


+28587 


+ 1-77852 


95 


+0071 


+1-5630 


2*6 


+7-57611 


-02 185 


+25334 


+ 1-80039 


100 


-0051 


+1-5622 


2'7 


+8-1 1035 


-01918 


+ 22008 


+1-81821 


110 


-0003 


+1-5799 


2'8 


+8-67930 


-01685 


+ 18649 


+ 1-83210 


120 


+ 0048 


+1-5640 


2'9 


+9-28602 


- -01482 


+15290 


+ 1-84219 


130 


0071 


+1-5737 


8'0 


+9-93383 


-01305 


+11963 


+1-84865 


140 


+0070 


+1-5721 


31 


+10-6263 


-01149 


+ -08699 


+1-85166 


150 


-0048 


+1-5662 


3*2 


+11-3673 


-01013 


+ -05526 


+ 1-85140 


160 


+0014 


+1-5769 


3*3 


+12-1610 


- -00894 


+ -02468 


+ 1-81808 


170 


+ 0020 


+ 1-5653 


3'4 


+13-0121 


-00789 


-00 152 


+1-84191 


180 


-0044 


+1-5741 


3'5 


+13-9254 


- -00697 


- -03213 


+ 1-83313 


190 


+0052 


+ 1-5704 


3'6 


+14-9063 


- -00616 


- -05797 


+ 1-82195 


200 


-0044 


+1-5684 


3*7 


+15-9606 


- -00545 


-08 190 


+ 1-80862 


300 


-0033 


+1-5709 


3*8 


+17-0948 


- -00482 


- -10378 


+1-79339 


400 


-0021 


+1-5721 


3-9 


+18-3157 


- -00427 


- -12350 


+ 1-77650 


500 


-0009 


+1-5726 


4-0 


+19-6309 


-00378 


- -14098 


+ 1-75820 


600 


+0001 


+1-5725 


41 


+21-0485 


- 00335 


-15617 


+ 1-73874 


700 


+0008 


+1-5720 


4'2 


+22-5774 


-00297 


- -16901 


+ 1-71837 


800 


+0011 


+1-5714 


4'3 


+24-2274 


- -00263 


-17951 


+ 1-69732 


900 


+0011 


+1-5707 


4'4 


+26-0090 


-00234 


- -18766 


+1-67583 


1000 


+0008 


+1-5702 


4'5 


+27-9337 


- -00207 


- -19349 


+ 1-65414 


2000 


+0005 


+1-5710 


4*6 


+30-0141 


-00181 


-1970S 


+ 1-63216 


3000 


+0001 


+1-5711 


4.7 


+32-2639 


-001 64 


-19839 


+1-61101 


4000 


-0002 


+1-5710 


4-8 


+34-6979 


-001 45 


-19760 


+1-58998 


5000 


-0002 


+1-5708 


4'9 


+37-3325 


-001 29 


- -19478 


+ 1-56956 


6000 


-0001 


+1-5706 


5'0 


+40-1853 


-00115 


-19003 


+1-54993 


7000 


+0001 


+1-5707 


6 


+85-990 


-00036 


-06806 


+ 1-42469 


8000 


+0001 


+1-5708 


7 


+ 191-50 


-00012 


+07670 


+1-45460 


9000 


+0001 


+1-5709 


8 


+440-38 


-00004 


+12243 


+1-57419 


10,000 


-0000 


+1-5709 


9 


+1037-9 


-00001 


+05535 


+1-66504 


100,000 


+0000 


+ 1-5708 


10 


+2492-2 


-00000 


-04546 


+1-65835 


1,000,000 


-oooo 


+ 1-5708 


11 


+6071-4 


-00000 


-08956 


+1-57831 








12 


+ 14960 


00000 


-04978 


+1-50497 








13 


+37198 


00000 


+02676 


+1'49936 








14 


+93193 


00000 


+06940 


+1-55621 








15 


+234956 


00000 


+04623 


+1-61819 









XXXVIL-BINOMIAL COEFFICIENTS FOR INTERPOLATION 
BY DIFFERENCES. 



t 


COEF 
A 2 


VS. OF 
A3 


t 


COEF] 

A 2 


PS. OF 
A 3 


t 


COKF 
A 2 


'3. OF 

A 3 


t 


CORFl 

A a 


PS. OF 
A 3 


01 


-005 


+ 003 


26 


-096 


+056 


51 


-125 


+062 


76 


-091 


+ 038 


02 


-010 


-f-006 


27 


-099 


+057 


52 


-125 


+062 


77 


-089 


+036 


03 


-015 


+ 010 


28 


-101 


+ 058 


53 


-125 


+061 


78 


-086 


+035 


04 


-019 


+013 


29 


-103 


+ 059 


54 


-121 


+060 


79 


-083 


+033 


05 


-024 


+015 


80 


-105 


+060 


55 


-124 


+060 


80 


-080 


+032 


06 


-028 


+018 


31 


-107 


+060 


-56 


-124 


+059 


81 


-077 


+031 


07 


-033 


+021 


32 


-109 


+061 


57 


-123 


+058 


82 


-074 


+029 


08 


-037 


+024 


33 


-111 


+062 


58 


-122 


+058 


83 


-071 


+028 


09 


-041 


+026 


34 


-112 


+ 062 


59 


-121 


+057 


84 


-067 


+026 


10 


-045 


+028 


35 


-114 


+063 


60 


-120 


+056 


85 


-064 


+024 


11 


-049 


+031 


36 


-115 


+063 


61 


-119 


+055 


86 


-060 


+023 


12 


-'053 


+033 


37 


-117 


+063 


62 


-118 


+054 


87 


-057 


+021 


13 


-057 


+035 


38 


-118 


+064 


63 


-117 


+053 


88 


-053 


+020 


14 


-060 


+037 


39 


-119 


+064 


64 


-115 


+052 


89 


-019 


+018 


15 


-064 


+039 


40 


-120 


+064 


65 


-114 


+051 


90 


-045 


+016 


16 


-067 


+041 


41 


-121 


+064 


66 


-112 


+050 


91 


-041 


+015 


17 


-071 


+043 


42 


-122 


+064 


67 


-111 


+049 


92 


- -037 


+013 


18 


-074 


+045 


43 


-123 


+064 


68 


-109 


+048 


93 


-033 


+012 


19 


-077 


+046 


44 


-123 


+064 


69 


-107 


+047 


94 


-028 


+010 


20 


-080 


+ 048 


45 


-124 


+064 


70 


-105 


+045 


95 ' 


-024 


+008 


21 


-083 


+049 


46 


-124 


+064 


71 


-103 


+044 


96 


-019 


+007 


22 


-086 


+051 


47 


-125 


+064 


72 


-101 


+043 


97 


-015 


+ 005 


23 


-089 


+052 


48 


-125 


+063 


73 


-099 


+042 


98 


-010 


+003 


24 


-091 


+053 


49 


-125 


+063 


74 


-096 


+040 


'99 


-005 


+002 


25 


-094 


+055 


50 


-125 


+ 063 


75 


-094 


+039 


1-00 


-000 


+000 



83 



XXXVIII. - PROPORTIONAL PARTS. 





X'l 


X'2 


x-3 


x-4 


x-5 


x-6 


X'7 


x*8 


X*9 


10 


1-0 


2-0 


3-0 


4-0 


5-0 


6-0 


7-0 


8-0 


9-0 


11 


M 


2-2 


3-3 


4.4 


5-5 


6-6 


7*7 


8-8 


9-9 


12 


1-2 


2-4 


3-6 


4*8 


6-0 


7-2 


8-4 


9-6 


10-8 


13 


1-3 


2-6 


3-9 


6-2 


G-5 


7-8 


9-1 


10-4 


11-7 


14 


1-4 


2-8 


4-2 


5-6 


7-0 


8-4 


9-8 


11-2 


12-6 


15 


1*5 


3-0 


4-5 


6-0 


7-5 


9-0 


10-5 


12*0 


13-5 


16 


1-6 


3-2 


4-8 


G-4 


8-0 


9-6 


11*2 


12-8 


14*4 


17 


1-7 


3-4 


5-1 


G-8 


8-5 


10-2 


11-9 


13'6 


15-3 


18 


1-8 


3'6 


6-4 


7-2 


9-0 


10-8 


12-6 


14-4 


16'2 


19 


1-9 


3-8 


5-7 


7'G 


9-5 


11-4 


13-3 


16-2 


17-1 


20 


2-0 


4-0 


6-0 


8-0 


10-0 


12-0 


14-0 


16-0 


18-0 


21 


2-1 


4-2 


6-3 


8-4 


10-5 


12-6 


14-7 


16-8 


18-9 


22 


2-2 


4.4 


6-6 


8-8 


11-0 


13*2 


15-4 


17-6 


19-8 


23 


2-3 


4-6 


G-9 


9*2 


11*5 


13-8 


1G-JL 


18'4 


20-7 


24 


2-4 


4-8 


7'2 


9-6 


12-0 


14-4 


16'8 


19-2 


21'6 


25 


2-5 


5-0 


7-5 


10-0 


12-5 


15-0 


17-6 


20-0 


22-5 


26 


2-6 


5-2 


7-8 


10-4 


13-0 


15-6 


18-2 


20*8 


23'4 


27 


2-7 


5-4 


8'1 


10-8 


135 


16-2 


18-9 


21'6 


243 


28 


2-8 


5-6 


8-4 


11-2 


14-0 


16-8 


19*6 


22-4 


25-2 


29 


2-9 


5-8 


8-7 


11-6 


14-5 


17-4 


20'3 


23*2 


26-1 


30 


3-0 


6-0 


9-0 


12.0 


15-0 


18-0 


21-0 


24'0 


27-0 


31 


3'1 


6-2 


9-3 


12'4 


15-5 


18'6 


21*7 


24'8 


27*9 


32 


3-2 


6-4 


9'G 


12*8 


16-0 


19*2 


22'4 


25' G 


28'8 


33 


3-3 


G-6 


9-9 


13'2 


1G-5 


19-8 


23-1 


26-4 


29*7 


34 


3-4 


G-8 


10-2 


13'G 


17-0 


20-4 


23-8 


27*2 


30-6 


35 


3'5 


7'0 


10-5 


14-0 


17-5 


21-0 


24-5 


28-0 


31-6 


36 


3'G 


7-2 


10-8 


14-4 


18-0 


21-6 


25-2 


28-8 


32'4 


37 


3-7 


7-4 


11-1 


14-8 


18-5 


22-2 


25-9 


29-6 


33-3 


38 


3'8 


7-G 


11-4 


15-2 


19-0 


22-8 


26-6 


30-4 


34-2 


39 


3'9 


7-8 


11-7 


15-6 


19-5 


23-4 


27'3 


31-2 


35-1 


40 


4-0 


8-0 


12-0 


1G-0 


20-0 


24-0 


28-0 


32-0 


36-0 


41 


4-1 


8-2 


12-3 


1G-4 


20-5 


24-6 


28-7 


32-8 


36'9 


42 


4-2 


8-4 


12-6 


1G-8 


21-0 


25-2 


29-4 


33'6 


37-8 


43 


4-3 


8-6 


12-9 


17-2 


21'5 


25-8 


30-1 


34-4 


38-7 


44 


4.4 


8-8 


13*2 


17'6 


22-0 


26-4 


308 


35*2 


39*6 


45 


4'5 


9-0 


13'5 


18'0 


22-5 


27'0 


31-5 


36-0 


40-5 


46 


4*6 


9-2 


13-8 


18'4 


23-0 


27'6 


32-2 


36-8 


41-4 


47 


4-7 


9-4 


14-1 


18*8 


23-5 


28'2 


32-9 


37-6 


42-3 


48 


4'8 


9-6 


14'4 


192 


24-0 


28'8 


33-6 


38-4 


43'2 


49 


4'9 


9-8 


14*7 


19-6 


24-5 


29-4 


34-3 


9'2 


44-1 


50 


5-0 


10-0 


15*0 


20-0 


25-0 


30-0 


35-0 


*0'0 


46-0 


51 


5-1 


10-2 


15-3 


20-4 


25-5 


30-6 


35-7 


40*8 


45-9 


52 


5-2 


10-4 


15*6 


20-8 


26-0 


31-2 


36'4 


41-6 


46-8 


53 


5*3 


10-6 


15'9 


21-2 


26-5 


31-8 


37*1 


42'4 


47'7 


54 


5-4 


10'8 


1G2 


21-6 


27-0 


32*4 


37-8 


43-2 


48*6 




















f 



PROPORTIONAL PARTS continued. 





X'l 


X*2 


x-3 


x-4 


x-5 


x-6 


x-7 


x'8 


x*9 


55 


5-5 


11-0 


1G-5 


22-0 


27-5 


33-0 


38-5 


44-0 


49-5 


56 


5-6 


11-2 


16-8 


22-4 


28-0 


33-6 


39-2 


44-8 


50-4 


57 


5-7 


11-4 


17-1 


22-8 


28*5 


34-2 


39'9 


45'G 


51-3 


58 


5-8 


11-6 


17-4 


23-2 


29-0 


34-8 


40'G 


46-4 


52-2 


59 


5-9 


11-8 


17-7 


23-6 


29-5 


35-4 


41-3 


47-2 


53-1 


60 


6-0 


12-0 


18'0 


24-0 


30-0 


36-0 


42-0 


48-0 


54-0 


61 


6-1 


12-2 


18-3 


24-4 


30-5 


3G-G 


42-7 


48'8 


54-9 


62 


6*2 


12-4 


18-6 


24-8 


31-0 


37-2 


43-4 


49-6 


55-8 


63 


6-3 


12-6 


18-9 


25-2 


31-5 


37'8 


44-1 


50-4 


5(5-7 


64 


6-4 


12-8 


19-2 


25-6 


82-0 


38-4 


44-8 


51-2 


57-G 


65 


6-5 


13-0 


19-5 


2G-0 


32-5 


39-0 


45-5 


52-0 


58-5 


66 


6-6 


13-2 


19-8 


2G-4 


33*0 


39-6 


4G-2 


52-8 


59-4 


67 


6-7 


13-4 


20-1 


26-8 


33-5 


40-2 


46-9 


53-6 


60-3 


68 


6-8 


13-G 


20-4 


27'2 


34-0 


40-8 


47-6 


54-4 


61-2 


69 


6-9 


13-8 


20-7 


27-G 


34-5 


41-4 


48*3 


65'2 


G2-1 


70 


7-0 


14-0 


21-0 


28-0 


35-0 


42-0 


49-0 


56-0 


G3-0 


71 


7-1 


14-2 


21-3 


28-4 


35-5 


42-G 


49-7 


56-8 


63-9 


72 


7-2 


14-4 


21-G 


28-8 


36-0 


43-2 


50-4 


57-G 


G4-8 


73 


7-3 


14-6 


21-0 


29-2 


3G-5 


43-8 


61-1 


68-4 


G5-7 


74 


7'4 


14-8 


22-2 


29'G 


37-0 


44-4 


51-8 


59-2 


GG-6 


75 


7-5 


15-0 


22-5 


30-0 


37-5 


45-0 


52-5 


GO'O 


67-5 


76 


7-6 


15'2 


22-8 


30-4 


38-0 


45-6 


5:5-2 


60-8 


68-4 


77 


7-7 


15-4 


23-1 


30-8 


38-5 


46-2 


53-9 


61-6 


G9-3 


78 


7-8 


15-6 


23-4 


31-2 


39-0 


46-8 


54-6 


f.2-4 


70-2 


79 


7-9 


15-8 


23-7 


31-6 


39 '5 


47-4 


55-3 


G3-2 


71*1 


80 


8-0 


16-0 


24-0 


320 


40-0 


48-0 


5G-0 


64-0 


72-0 


81 


8-1 


16-2 


24-3 


32-4 


40-5 


48-G 


56-7 


C4-8 


72-9 


82 


8-2 


16*4 


24-G 


32-8 


41-0 


49-2 


57-4 


G5-6 


73-8 


83 


8-3 


16-6 


24-9 


33-2 


41-5 


49-8 


58-1 


GG-4 


74-7 


84 


8-4 


16-8 


25-2 


33-G 


42-0 


60-4 


58-8 


G7-2 


76-6 


85 


8-5 


17'0 


25-5 


34-0 


42-5 


51-0 


69-5 


G8'0 


7G-5 


86 


8-6 


17-2 


25-8 


34-4 


43-0 


51-6 


60-2 


68-8 


77-4 


87 


8-7 


17-4 


26-1 


34-8 


43-5 


52-2 


60-9 


G9-G 


78-3 


88 


8-8 


17-G 


26-4 


35-2 


44-0 


62-8 


61-6 


70-4 


79-2 


89 


8-9 


17-8 


26-7 


35'G 


44-5 


53-4 


62'3 


71-2 


80-1 


90 


9-0 


18-0 


27-0 


36-0 


45-0 


54' 


G3'0 


72-0 


81-0 


91 


9-1 


18-2 


27-3 


36'4 


45-5 


54-6 


63-7 


72-8 


81-9 


92 


9-2 


18-4 


27-6 


3G-8 


46-0 


55*2 


64-4 


73-6 


82-8 


93 


9-3 


18-6 


27-9 


37-2 


46-5 


55-8 


65-1 


74-4 


83-7 


94 


9-4 


18-8 


28-2 


37-6 


47-0 


5G-4 


65-8 


75-2 


84-G 


95 


9-5 


19-0 


28-5 


38-0 


47*5 


57-0 


66-5 


76-0 


85-5 


96 


9*6 


19*2 


28-8 


38-4 


48-0 


57-6 


67-2 


76-8 


86-4 


97 


9-7 


19'4 


29-1 


38-8 


48-5 


58-2 


67-9 


77-6 


87-3 


98 


9-8 


19-6 


29-4 


39-2 


49-0 


58-8 


68-G 


78-4 


88-2 


99 


9'9 


19-8 


29-7 


39-6 


49-5 


59-4 


60-3 


79-2 


89-1 



9 o 



XXXIX. NUMBERS USED IN CALCULATIONS. 

v = Ratio of Circumference of a Circle to Diameter. 
e - Base of Natural Logarithms. 



NUMBKHS. 

TT = 3-14159 20536 

2r= 0-28318 63072 

47T = 12-50037 06144 

\* = 1-57079 03208 

|ir= 1-04719 75512 

}* = 0-78539 81034 

ITT^ 0-52359 87756 

1^= 0-01745 32925 

isio^- 0-00029 08882 

(mfooo" O'OOOOO 48481 

1= 4-18879 02048 

l4-ir = 0-31830 98802 

180 4- = 57-29577 95131 

6-18000 4- TT = 200204-80625 

1-4-4* = 0-07957 74715 

1 -*- 67T = 0-05305 16477 

*= 9-86960 44011 

1 4- 7T 2 = 0-10132 11836 

V*= 1-77245 38509 

1 4- V = 56418 95835 

y= 1-40459 18876 

i!/7r 2 = 214502 93971 

5/(64-)= 1-24070 09818 

iy(C7T 2 )= 3-89777 70897 

i = 4-83597 58020 



e = 2-71828 
Log 10 e= '43429 
Log10 = 2-30258 

= 1-0010005 
: 1-0020020 
= 1-0030045 
= 1-0040080 
: 1-0050125 
: 1-0060180 
: 1-0070245 
= 1-0080320 
: 1-0090405 



LOGARITHMS. 

0-49714 98727 

0-79817 98684 

1-09920 98640 

0-19611 98770 

0-02002 86180 

1-89508 98814 

1-71899 86223 

2-24187 73676 

4-46372 61172 

G-08557 48068 

0-02208 80093 

1-50285 01273 

1-75812 20324 

5-31442 51332 

2-90079 013GO 

2-72469 88769 



0-99429 
1 00570 
0-24857 
1-75142 
0-16571 
0-33143 
0-09366 
0-59081 
0-68448 



97454 
02516 
49363 
50637 
66242 
32485 
71259 
69986 
41244 



c .oos 
e .oo9 



18285 

44819 

50930 

f .001 - -9990005 
e -.oo2 = -9980020 
e--w3 ~ -9970045 
e ~.oo* = -9960080 
e-(X)5 = -9950125 
e- 000 = -9940180 
e-w - -9930245 
6 -.oos = -9920320 
c-009 . -9910405 
e -.ooor = l _ 



e = 2 3141 x 10 

** = 5-3549 x 10 1 
3 = 1-2392 x 10 4 
e 4 * = 2-8675 x 10 6 
e&r = 6-6356 X 10 8 

V 

e 2 ^ 4-8105 
2 = 1-1132 x 10 1 

6ir 

2 = 2-5760 x 10 9 
e2 = 5-9610 xlO< 

9ir 

2 = 1-3794 x 10" 
e* = 21933 

Sir 

* = 1-0551 x 10 

for 

e 4 =5-0754x10 
c v = 2-4415 x 10* 

9>r 

c 4 = 1-1745 xlO 3 

llir 

4 = 5-6498 x 10 3 
c 4 " = 2-7178 x 10* 
e 4 = 1-3074 x 10* 
4 = 6-2893 x 10* 

19rr 

e 4 = 3-0205 x 10 6 



- = 4-3214 x 10" 1 
6-2, - 1-8674 x 10- 
-fc = 8-0699 x 10' 
-* = 3-4873 x 10~ 
e-5 = 1-5070 X 10f 


e" 2 = 2-0788 x 10~> 

Sir 

" "2" =8-9833 xlO- 1 

6ir 

e" 2 = 3-8820 x 10" 4 

_7ir 

e" 2 = 1-6776 x 10~* 
- 9ir 
" 2 = 7-2495 x 10-' 

tr 

6"" 4 "= 4-5594 xlO- 1 

Sir 

e 4 = 9-4780 x 10- 8 

5n- 

e 4 " = 1-9703 x 10-* 

- 7tr 
i 4 = 4-0958 x 10-* 

9? 

c" * = 8-5144 x 10' 4 



HIT 
""*" = 



= 1-7700 x 10~ 4 

13* 

T 4 = 3-6794 x 10" 

15JT 

e" 4 = 7-6487 X lO" 1 

ITjr 

" 4 = 1-5900 X 10^ 

I9rr 

t 4 = 3-3053 x 10- T 



EULBR'S NUMBERS B.. 



E 3 = 6-1 x 10 
E, = 1-385 x 10* 
E c = 5-0521 x 10 4 



E 6 = 2-702765 x 10 fl 
E 7 = 1-99360981 x 10 8 
E 8 = 1-9391512145 x 10* 
E 9 = 2-404879675441 x 1C 11 



EULER'S CONSTANT 



= 57721 56649 



92 



VALUES OP 8 W , s n , T., V w . 



8, B 1-* -f 2- + 3"* -f . . , T n = 1- + 3~" + 5- 4- . . . 
s= l - 2-" + 3"* - . . , V w = 1-* - 3"* 4- 5-* + . . . 


n 


s. 


> 


T. 


I 
2 
3 
4 
5 


00 

1-64493 40668 
1-20205 69032 
1-08232 32337 
1-03692 77551 


69314 71806 
82246 70334 
90154 26774 
94703 28295 
97211 97704 


00 

1-23370 05501 
1-05179 97903 
1-01467 80316 
1-00452 37628 


6 
7 
8 
9 
10 


1-01734 30620 
1-00834 92774 
1-00407 73562 
1-00200 83928 
1-00099 45751 


98555 10913 
-99259 38199 
99623 30019 
99809 42975 
99903 95076 


1-00144 70766 
1-00047 15487 
1-00016 51790 
1-00005 13452 
1-00001 70414 


11 

12 
13 
14 
15 


1-00049 41886 
1-00024 60866 
100012 27133 
1-00006 12481 
1-00003 05882 


99951 71435 
99975 76851 
99987 85428 
99993 91703 
99996 95512 


1-00000 56661 
1-00000 18858 
1-00000 06281 
1-00000 02092 
1-00000 00697 


16 
17 

id 

19 
20 


1-00001 52823 
1-00000 76372 
1-00000 38173 
1-00000 19082 
1-00000 09540 


99998 47642 
99999 23783 
99999 61879 
99999 80935 
-99999 90466 


1-00000 00232 
1-00000 00077 
1-00000 00026 
1-00000 00009 
1-00000 00003 



ENGLISH AND METRIC EQUIVALENTS. 



1 Metre (0 0.) 
1 Square metre 
1 Cubic decimetre 
1 Litre 
1 Kilogram 
1 Gramme 



lYard 

1 Cubic inch 

1 Gallon 

1 Pound (avoir.) 



= 39*370113 inches (62 F.) 
= 10-7639 square feet 
= 61*024 cubic inches 
= 1*7598 pints 
- 2'2046223 pounds (avoir.) 
= 15-4323564 grains 



= 0'914399 metres 

= 16*387 cubic centimetres 

= 4-5459631 litres 

= 0-45359243 kilograms 



PRINTED BY WILLIAM CLOWES AND SONS, LIMITED, LONDON AND BECCLES.